When Math Met Origami | Robert Lang | Google Zeitgeist

When Math Met Origami | Robert Lang | Google Zeitgeist


I want to introduce Robert Lang. Robert is
a full-time origami artist and consultant. So for of us who think paper is
a dead medium, he’s got other ideas for us. Before he became — his work
has been shown in New York at the Museum of Modern Art and in Paris at the
Carrousel du Louvre, at the Peabody Essex Museum in Salem, in Japan at
the Nippon Museum of Origami, among other places.
Before he got into doing origami full time, he was a physicist, an engineer, an
R&D manager. He has authored or coauthored over 80 technical publications
and has 50 patents awarded to him or pending on semiconductors,
semiconductor lasers, optics, and integrated optic electronics. Robert?
>>Robert Lang: Thank you. I will say if you are ever wondering how to
make a physicist feel inadequate, put him after Murray Gell-Mann and Andrew
Lankford. So I’m not going to talk about physics. I am going to tell you a
story. I am going to talk about how flapping birds are connected to space
telescopes. That sounds pretty strange because flapping birds, that’s origami,
Japanese paper folding art, simple things, trivial things, birds, bunnies, cuddy
catchers. It has been simple and trivial for hundreds of years in Japan. It
might have stayed simple and trivial forever but for this man. Akiro
Yoshizawa in the middle of the 20th century took up his country’s folk art and
began creating new figures. But he did something even more important. He
created a language for communication of origami. And as Sebastian told us,
once you have language, you can do amazing things. That language was the
catalyst. It let people come up with something, build upon it, teach it to
someone else who could build. And this kicked off an exponential growth of
this Japanese folding art. It took origami away from those simple beginnings
to some place very different, someplace like this, because this,
too, is origami. This is one uncut sheet of paper. This is
one of my designs from a while back, but it has got a lot of details. It
tells the correct time twice a day. [ Laughter ]
And there are thousands of other origami designs. So all this comes together
to raise a new question, “What changed?” And what changed — what was the mindshift
of origami was that math came to origami. And that’s what I want to tell
you about. How does it enter in? Well, this is a simple
origami design. It’s got two folds in it, two different types of folds. One that
pokes up. It is called a mountain fold. And one that pokes down called a valley
fold. Every origami figure, no matter how complicated,
is nothing more than mountains and valley folds. So when you want
a design an origami figure, you design this pattern, this crease pattern,
the pattern of the folds. How would we do that? How would math enter
in? Let me show you the equation of origami. You start with an idea,
you add it to square and you get a folded shape. That’s it.
[ Laughter ] Well, no, not really. What do we mean by these
symbols? And can I be — and can I be that specific? This is not just
a random bug. This is a stag beetle. Can we be that specific about what
we want? The answer is, yeah, we can. How do we do it?
Let me go back to that equation. I’m going to stretch it out, and I’m going to
start from the end. If I want to end with a folded shape of a stag beetle, first I
need a configuration of the paper that has a flap for the legs and a flap for the
antenna, a flap for the jaws. How would I describe that configuration that I
need? Well, I could draw a stick figure where every
line tells me a flap and how they’re connected and how long they are. And
that stick figure comes from the subject.
Now, if I want to go forward, that first step of drawing the stick figure, that’s
pretty easy. Kids do that. And that last step of bending legs to be zig-zaggy
and making antennas skinny, that’s easy, too. But that middle step, that’s the
hard step. But that is exactly the step where math enters in, can get us over
the hump and complete the creative arc. So let’s look at that hard step. I’ve got
a stick figure. And I want to make a collection of flaps. And what we do in science
is when we have a hard problem like how do you make a bunch of flaps,
we look at the easiest version of that problem. And the easiest version of
that problem is how do you make one flap? So let’s look at that. I give you
all paper and I say, make me a flap. It is a long skinny bit of paper. And you
will fold it in half a couple times until it
is long and skinny and then say, That’s my flap. The end of it is my flap.
If I say, How much paper went into the flap? You could unfold it and look at
the crease pattern and you’d see that the upper left corner is the paper that
went into the flap. And if I ask what is the minimum amount of
paper you need to do that, well, you would make it skinnier and skinnier and
find the minimum amount of paper that goes into a flap for the skinniest
possible flap is a quarter circle. So a quarter circle of paper gives you a flap.
What if that flap comes not from the corner but from somewhere else? You
go through the same process. You find it comes from a half circle or a middle
circle. So no matter where a flap comes from, it needs a circular region of
paper. Now we can go back to the hard problem. What
do we use if we want to make a bunch of flaps? The answer is a bunch
of circles. And it seems so obvious now, but this was
a revolution in the world of origami because once people realized to design something
like an eight-legged spider you find a packing of eight circles, that
packing gave you the master plan for all of the creases that you need. That crease
pattern was guaranteed to fold into a base. The base was guaranteed to fold
into the thing you were after, be it a spider. And sure enough, you could make
a spider. And if an eight-legged spider wasn’t what
you wanted, you wanted a ten- limbed dragonfly, you could do that.
Make a preying mantis. If folding a single preying mantis from an uncut
square of paper wasn’t interesting enough, well, then you could do two
preying mantises from a single uncut square of paper.
But not just insects. We do — oh, we could do deer. If you want a different
branching pattern, fold an elk. If we have any Canadians, we could do a
moose. We can do animals of all types, and we can put detail in to give life.
There is a dancing crane. There is one of these on display out in the hall. Or
put claws on a Grizzly bear or toes and eyes on a tree frog.
We can do two figures from a single sheet of paper, a man with a guitar or a
man with a bass. If you think a guitar or a bass isn’t an interesting enough
instrument, can we do more interesting instruments? Yeah, we can. But not
just representational folding. Origami has shifted to the abstract. So we can
make geometrical shapes, stars, rosets, things that don’t look like something
but that are beautiful on their own. And this aspect of origami has its roots in
computer science. Ron Resch, a computer scientist and artist, developed and
patented two-dimensional crease patterns and folds way back in the ’60s. And
people still fold his designs today.
These are some of the things he did. And when you look at these, you think,
you know, they are not just interesting and beautiful but these could actually
be useful, domes or building structures, other shapes.
And, indeed, origami and math has turned out to have applications in the real
world throughout. So Koryo Miura, Japanese engineer, studied this pattern
that opens and closed and realized this has the right properties to make a
solar array. So this folding pattern was adapted for a solar array that flew in
1995. We in the U.S., we make folding structures.
The James Webb Space Telescope has two folds in it. You don’t need
an origami artist to tell you how to put two folds in. But the reason it folds
is because it has to be small for the journey to fit inside a rocket and big and
flat at the destination. And whenever you have those two requirements,
folding can provide a solution. Engineers at the Lawrence Livermore
Lab had their eyes set on a somewhat larger telescope. Ultimately a 100-meter
telescope, not 100 meters long, 100-meter diameter lens. So this
would need a more complicated folding pattern.
So, they got in touch with me and I worked with them. And we came up with
this pattern that unfolds from a flat ring to a cylinder and you can just keep
scaling this by adding more and more rings and make any size telescope lens
you want. And here’s the first telescope lens on its test range at Livermore, 5-
meter lens, twice the size of the Hubble Space Telescope.
But you can do more than just lenses. Japan has made solar sails that
unfold as they deploy. At the very opposite end of the size scale,
Caltech physicist Paul Rothemund has developed techniques to fold DNA into
shapes. Why would you want to fold DNA, besides making smiley faces and
stars? Well, to make containers for drugs, for drug delivery. And in the medical
applications, Zhong You at Oxford University developed a heart stent,
a tube that holds open a blocked artery that folds down using an origami pattern
because it too has to be small for the journey and large for the destination.
One of the most unusual applications came in the design of air bags.
Automotive air bag designers have to make their airbags work under many
conditions. Instead of crashing cars, you do simulation. But they had a
problem. How do you flatten the air bag in the simulation?
It turns out that the folds you need, the folding pattern, are exactly the folds
and the patterns that come from those insect designs that I showed earlier.
So armed with the origami algorithms, air bag designers could design their
airbags, do their simulations. There’s — I could go on about this. I don’t
have time to do that. So what I want to do instead is I want to leave you
with a question and thought which is: Where did these applications come from?
So let me look at that heart stent. That heart stent was based on what’s
called the water bomb base. It is the folding pattern used for that blowup
bunny I showed early on, that little blowup box everyone makes.
The reason they could use that is because people studied the mathematics of
that folding pattern. Where did that air bag flattening algorithm come from? It
came because people had studied the math to design insects, to figure out
how to fold anything out of paper. And so these two examples illustrate a really
powerful principle that happens in the arts, in the science, especially in
math, that problems you solve for their own sake because they’re merely interesting,
very often turn out down the road to have a real-live practical application.
And in the case of origami, some of those problems might even save a life.
Thank you. [ Applause ]

22 thoughts on “When Math Met Origami | Robert Lang | Google Zeitgeist

  1. If you enjoyed this I highly recommend you to watch the documentary between the folds, where masters as Lang and among others share their thoughts and greatness 🙂

  2. WOW! His voice is like a school professor. I almost fel asleep. I need to get back in school. Listening to him made me think about the things I don't know. Ugh. LOL

  3. Had the chance to hear him speak at a talk, and he's penrose tessellation was expecially mesmerizing. I'm so glad that I got to meet him 😀

  4. THANK YOU SO MUCH you saved me on a last minute what does origami have to do with math thanks:) lol

  5. well what´s there to say ; the one and only Robert Lang Mr Origami himself. just love they guy ,even though i never met him in person and i probably never will either .But ive seen many videos with him ,awesome guy at his work .

  6. See him many times, its too technical. He make a book to design. But its only a start and you will need to study more thereafter. Anyway there many other designers like Tomohiro; they all use different mindset. ex a nice way to use 22.5 and 45s but know were to put the molecule. Everyone has different approach some use grid some not even circle pack. But its has to be shaped to design even after you have the pattern done.

  7. i want To know why Robert Lang and Brian Chan both publish c.p's With circle packing..yet no one has done a tutorial tackling circle packing on paper

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