00:00:18
My talk is "Flapping Birds and Space Telescopes."
00:00:21
And you would think that should have nothing to do with one another,
00:00:23
but I hope by the end of these 18 minutes,
00:00:26
you'll see a little bit of a relation.
00:00:29
It ties to origami. So let me start.
00:00:30
What is origami?
00:00:32
Most people think they know what origami is. It's this:
00:00:35
flapping birds, toys, cootie catchers, that sort of thing.
00:00:38
And that is what origami used to be.
00:00:40
But it's become something else.
00:00:42
It's become an art form, a form of sculpture.
00:00:44
The common theme -- what makes it origami --
00:00:46
is folding is how we create the form.
00:00:50
You know, it's very old. This is a plate from 1797.
00:00:53
It shows these women playing with these toys.
00:00:55
If you look close, it's this shape, called a crane.
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Every Japanese kid
00:01:00
learns how to fold that crane.
00:01:02
So this art has been around for hundreds of years,
00:01:04
and you would think something
00:01:06
that's been around that long -- so restrictive, folding only --
00:01:09
everything that could be done has been done a long time ago.
00:01:12
And that might have been the case.
00:01:14
But in the twentieth century,
00:01:16
a Japanese folder named Yoshizawa came along,
00:01:19
and he created tens of thousands of new designs.
00:01:22
But even more importantly, he created a language,
00:01:25
a way we could communicate,
00:01:27
a code of dots, dashes and arrows.
00:01:29
Harkening back to Susan Blackmore's talk,
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we now have a means of transmitting information
00:01:33
with heredity and selection,
00:01:36
and we know where that leads.
00:01:38
And where it has led in origami
00:01:40
is to things like this.
00:01:42
This is an origami figure --
00:01:44
one sheet, no cuts, folding only, hundreds of folds.
00:01:50
This, too, is origami,
00:01:52
and this shows where we've gone in the modern world.
00:01:55
Naturalism. Detail.
00:01:57
You can get horns, antlers --
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even, if you look close, cloven hooves.
00:02:01
And it raises a question: what changed?
00:02:04
And what changed is something
00:02:06
you might not have expected in an art,
00:02:09
which is math.
00:02:11
That is, people applied mathematical principles
00:02:13
to the art,
00:02:16
to discover the underlying laws.
00:02:18
And that leads to a very powerful tool.
00:02:21
The secret to productivity in so many fields --
00:02:23
and in origami --
00:02:25
is letting dead people do your work for you.
00:02:28
(Laughter)
00:02:29
Because what you can do is
00:02:31
take your problem,
00:02:33
and turn it into a problem that someone else has solved,
00:02:36
and use their solutions.
00:02:38
And I want to tell you how we did that in origami.
00:02:41
Origami revolves around crease patterns.
00:02:43
The crease pattern shown here is the underlying blueprint
00:02:46
for an origami figure.
00:02:48
And you can't just draw them arbitrarily.
00:02:50
They have to obey four simple laws.
00:02:53
And they're very simple, easy to understand.
00:02:55
The first law is two-colorability. You can color any crease pattern
00:02:58
with just two colors without ever having
00:03:00
the same color meeting.
00:03:03
The directions of the folds at any vertex --
00:03:06
the number of mountain folds, the number of valley folds --
00:03:09
always differs by two. Two more or two less.
00:03:11
Nothing else.
00:03:13
If you look at the angles around the fold,
00:03:15
you find that if you number the angles in a circle,
00:03:17
all the even-numbered angles add up to a straight line,
00:03:20
all the odd-numbered angles add up to a straight line.
00:03:23
And if you look at how the layers stack,
00:03:25
you'll find that no matter how you stack folds and sheets,
00:03:28
a sheet can never
00:03:30
penetrate a fold.
00:03:32
So that's four simple laws. That's all you need in origami.
00:03:35
All of origami comes from that.
00:03:37
And you'd think, "Can four simple laws
00:03:39
give rise to that kind of complexity?"
00:03:41
But indeed, the laws of quantum mechanics
00:03:43
can be written down on a napkin,
00:03:45
and yet they govern all of chemistry,
00:03:47
all of life, all of history.
00:03:49
If we obey these laws,
00:03:51
we can do amazing things.
00:03:53
So in origami, to obey these laws,
00:03:55
we can take simple patterns --
00:03:57
like this repeating pattern of folds, called textures --
00:04:00
and by itself it's nothing.
00:04:02
But if we follow the laws of origami,
00:04:04
we can put these patterns into another fold
00:04:07
that itself might be something very, very simple,
00:04:09
but when we put it together,
00:04:11
we get something a little different.
00:04:13
This fish, 400 scales --
00:04:16
again, it is one uncut square, only folding.
00:04:20
And if you don't want to fold 400 scales,
00:04:22
you can back off and just do a few things,
00:04:24
and add plates to the back of a turtle, or toes.
00:04:27
Or you can ramp up and go up to 50 stars
00:04:30
on a flag, with 13 stripes.
00:04:33
And if you want to go really crazy,
00:04:36
1,000 scales on a rattlesnake.
00:04:38
And this guy's on display downstairs,
00:04:40
so take a look if you get a chance.
00:04:43
The most powerful tools in origami
00:04:45
have related to how we get parts of creatures.
00:04:48
And I can put it in this simple equation.
00:04:50
We take an idea,
00:04:52
combine it with a square, and you get an origami figure.
00:04:55
(Laughter)
00:04:59
What matters is what we mean by those symbols.
00:05:01
And you might say, "Can you really be that specific?
00:05:04
I mean, a stag beetle -- it's got two points for jaws,
00:05:06
it's got antennae. Can you be that specific in the detail?"
00:05:10
And yeah, you really can.
00:05:13
So how do we do that? Well, we break it down
00:05:16
into a few smaller steps.
00:05:18
So let me stretch out that equation.
00:05:20
I start with my idea. I abstract it.
00:05:23
What's the most abstract form? It's a stick figure.
00:05:26
And from that stick figure, I somehow have to get to a folded shape
00:05:29
that has a part for every bit of the subject,
00:05:32
a flap for every leg.
00:05:34
And then once I have that folded shape that we call the base,
00:05:37
you can make the legs narrower, you can bend them,
00:05:40
you can turn it into the finished shape.
00:05:42
Now the first step, pretty easy.
00:05:44
Take an idea, draw a stick figure.
00:05:46
The last step is not so hard, but that middle step --
00:05:49
going from the abstract description to the folded shape --
00:05:52
that's hard.
00:05:54
But that's the place where the mathematical ideas
00:05:56
can get us over the hump.
00:05:58
And I'm going to show you all how to do that
00:06:00
so you can go out of here and fold something.
00:06:02
But we're going to start small.
00:06:04
This base has a lot of flaps in it.
00:06:06
We're going to learn how to make one flap.
00:06:09
How would you make a single flap?
00:06:11
Take a square. Fold it in half, fold it in half, fold it again,
00:06:14
until it gets long and narrow,
00:06:16
and then we'll say at the end of that, that's a flap.
00:06:18
I could use that for a leg, an arm, anything like that.
00:06:21
What paper went into that flap?
00:06:23
Well, if I unfold it and go back to the crease pattern,
00:06:25
you can see that the upper left corner of that shape
00:06:28
is the paper that went into the flap.
00:06:30
So that's the flap, and all the rest of the paper's left over.
00:06:33
I can use it for something else.
00:06:35
Well, there are other ways of making a flap.
00:06:37
There are other dimensions for flaps.
00:06:39
If I make the flaps skinnier, I can use a bit less paper.
00:06:42
If I make the flap as skinny as possible,
00:06:45
I get to the limit of the minimum amount of paper needed.
00:06:48
And you can see there, it needs a quarter-circle of paper to make a flap.
00:06:52
There's other ways of making flaps.
00:06:54
If I put the flap on the edge, it uses a half circle of paper.
00:06:57
And if I make the flap from the middle, it uses a full circle.
00:07:00
So, no matter how I make a flap,
00:07:02
it needs some part
00:07:04
of a circular region of paper.
00:07:06
So now we're ready to scale up.
00:07:08
What if I want to make something that has a lot of flaps?
00:07:11
What do I need? I need a lot of circles.
00:07:15
And in the 1990s,
00:07:17
origami artists discovered these principles
00:07:19
and realized we could make arbitrarily complicated figures
00:07:22
just by packing circles.
00:07:25
And here's where the dead people start to help us out,
00:07:28
because lots of people have studied
00:07:31
the problem of packing circles.
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I can rely on that vast history of mathematicians and artists
00:07:36
looking at disc packings and arrangements.
00:07:39
And I can use those patterns now to create origami shapes.
00:07:43
So we figured out these rules whereby you pack circles,
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you decorate the patterns of circles with lines
00:07:48
according to more rules. That gives you the folds.
00:07:50
Those folds fold into a base. You shape the base.
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You get a folded shape -- in this case, a cockroach.
00:07:57
And it's so simple.
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(Laughter)
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It's so simple that a computer could do it.
00:08:05
And you say, "Well, you know, how simple is that?"
00:08:07
But computers -- you need to be able to describe things
00:08:09
in very basic terms, and with this, we could.
00:08:12
So I wrote a computer program a bunch of years ago
00:08:14
called TreeMaker, and you can download it from my website.
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It's free. It runs on all the major platforms -- even Windows.
00:08:19
(Laughter)
00:08:21
And you just draw a stick figure,
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and it calculates the crease pattern.
00:08:25
It does the circle packing, calculates the crease pattern,
00:08:28
and if you use that stick figure that I just showed --
00:08:30
which you can kind of tell, it's a deer, it's got antlers --
00:08:33
you'll get this crease pattern.
00:08:35
And if you take this crease pattern, you fold on the dotted lines,
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you'll get a base that you can then shape
00:08:40
into a deer,
00:08:42
with exactly the crease pattern that you wanted.
00:08:44
And if you want a different deer,
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not a white-tailed deer, but you want a mule deer, or an elk,
00:08:49
you change the packing,
00:08:51
and you can do an elk.
00:08:53
Or you could do a moose.
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Or, really, any other kind of deer.
00:08:57
These techniques revolutionized this art.
00:09:00
We found we could do insects,
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spiders, which are close,
00:09:04
things with legs, things with legs and wings,
00:09:08
things with legs and antennae.
00:09:10
And if folding a single praying mantis from a single uncut square
00:09:13
wasn't interesting enough,
00:09:15
then you could do two praying mantises
00:09:17
from a single uncut square.
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She's eating him.
00:09:21
I call it "Snack Time."
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And you can do more than just insects.
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This -- you can put details,
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toes and claws. A grizzly bear has claws.
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This tree frog has toes.
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Actually, lots of people in origami now put toes into their models.
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Toes have become an origami meme,
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because everyone's doing it.
00:09:41
You can make multiple subjects.
00:09:43
So these are a couple of instrumentalists.
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The guitar player from a single square,
00:09:48
the bass player from a single square.
00:09:50
And if you say, "Well, but the guitar, bass --
00:09:52
that's not so hot.
00:09:54
Do a little more complicated instrument."
00:09:56
Well, then you could do an organ.
00:09:58
(Laughter)
00:10:01
And what this has allowed is the creation
00:10:03
of origami-on-demand.
00:10:05
So now people can say, "I want exactly this and this and this,"
00:10:08
and you can go out and fold it.
00:10:11
And sometimes you create high art,
00:10:13
and sometimes you pay the bills by doing some commercial work.
00:10:16
But I want to show you some examples.
00:10:18
Everything you'll see here,
00:10:20
except the car, is origami.
00:10:23
(Video)
00:10:51
(Applause)
00:10:54
Just to show you, this really was folded paper.
00:10:57
Computers made things move,
00:10:59
but these were all real, folded objects that we made.
00:11:03
And we can use this not just for visuals,
00:11:06
but it turns out to be useful even in the real world.
00:11:09
Surprisingly, origami
00:11:10
and the structures that we've developed in origami
00:11:13
turn out to have applications in medicine, in science,
00:11:16
in space, in the body, consumer electronics and more.
00:11:19
And I want to show you some of these examples.
00:11:22
One of the earliest was this pattern,
00:11:24
this folded pattern,
00:11:26
studied by Koryo Miura, a Japanese engineer.
00:11:29
He studied a folding pattern, and realized
00:11:31
this could fold down into an extremely compact package
00:11:34
that had a very simple opening and closing structure.
00:11:37
And he used it to design this solar array.
00:11:40
It's an artist's rendition, but it flew in a Japanese telescope
00:11:43
in 1995.
00:11:45
Now, there is actually a little origami
00:11:47
in the James Webb Space Telescope, but it's very simple.
00:11:50
The telescope, going up in space,
00:11:52
it unfolds in two places.
00:11:55
It folds in thirds. It's a very simple pattern --
00:11:57
you wouldn't even call that origami.
00:11:59
They certainly didn't need to talk to origami artists.
00:12:02
But if you want to go higher and go larger than this,
00:12:05
then you might need some origami.
00:12:07
Engineers at Lawrence Livermore National Lab
00:12:09
had an idea for a telescope much larger.
00:12:12
They called it the Eyeglass.
00:12:14
The design called for geosynchronous orbit
00:12:16
25,000 miles up,
00:12:18
100-meter diameter lens.
00:12:21
So, imagine a lens the size of a football field.
00:12:24
There were two groups of people who were interested in this:
00:12:26
planetary scientists, who want to look up,
00:12:29
and then other people, who wanted to look down.
00:12:33
Whether you look up or look down,
00:12:35
how do you get it up in space? You've got to get it up there in a rocket.
00:12:38
And rockets are small. So you have to make it smaller.
00:12:41
How do you make a large sheet of glass smaller?
00:12:43
Well, about the only way is to fold it up somehow.
00:12:46
So you have to do something like this.
00:12:48
This was a small model.
00:12:51
Folded lens, you divide up the panels, you add flexures.
00:12:53
But this pattern's not going to work
00:12:56
to get something 100 meters down to a few meters.
00:12:59
So the Livermore engineers,
00:13:01
wanting to make use of the work of dead people,
00:13:03
or perhaps live origamists, said,
00:13:06
"Let's see if someone else is doing this sort of thing."
00:13:09
So they looked into the origami community,
00:13:12
we got in touch with them, and I started working with them.
00:13:14
And we developed a pattern together
00:13:16
that scales to arbitrarily large size,
00:13:18
but that allows any flat ring or disc
00:13:22
to fold down into a very neat, compact cylinder.
00:13:25
And they adopted that for their first generation,
00:13:27
which was not 100 meters -- it was a five-meter.
00:13:29
But this is a five-meter telescope --
00:13:31
has about a quarter-mile focal length.
00:13:33
And it works perfectly on its test range,
00:13:35
and it indeed folds up into a neat little bundle.
00:13:39
Now, there is other origami in space.
00:13:41
Japan Aerospace [Exploration] Agency flew a solar sail,
00:13:44
and you can see here that the sail expands out,
00:13:47
and you can still see the fold lines.
00:13:49
The problem that's being solved here is
00:13:52
something that needs to be big and sheet-like at its destination,
00:13:55
but needs to be small for the journey.
00:13:57
And that works whether you're going into space,
00:14:00
or whether you're just going into a body.
00:14:03
And this example is the latter.
00:14:05
This is a heart stent developed by Zhong You
00:14:08
at Oxford University.
00:14:10
It holds open a blocked artery when it gets to its destination,
00:14:13
but it needs to be much smaller for the trip there,
00:14:16
through your blood vessels.
00:14:18
And this stent folds down using an origami pattern,
00:14:21
based on a model called the water bomb base.
00:14:25
Airbag designers also have the problem
00:14:27
of getting flat sheets
00:14:29
into a small space.
00:14:32
And they want to do their design by simulation.
00:14:34
So they need to figure out how, in a computer,
00:14:36
to flatten an airbag.
00:14:38
And the algorithms that we developed
00:14:40
to do insects
00:14:42
turned out to be the solution for airbags
00:14:45
to do their simulation.
00:14:47
And so they can do a simulation like this.
00:14:50
Those are the origami creases forming,
00:14:52
and now you can see the airbag inflate
00:14:54
and find out, does it work?
00:14:57
And that leads
00:14:59
to a really interesting idea.
00:15:01
You know, where did these things come from?
00:15:04
Well, the heart stent
00:15:06
came from that little blow-up box
00:15:08
that you might have learned in elementary school.
00:15:11
It's the same pattern, called the water bomb base.
00:15:14
The airbag-flattening algorithm
00:15:16
came from all the developments
00:15:18
of circle packing and the mathematical theory
00:15:21
that was really developed
00:15:23
just to create insects -- things with legs.
00:15:27
The thing is, that this often happens
00:15:29
in math and science.
00:15:31
When you get math involved, problems that you solve
00:15:34
for aesthetic value only,
00:15:36
or to create something beautiful,
00:15:38
turn around and turn out
00:15:40
to have an application in the real world.
00:15:43
And as weird and surprising as it may sound,
00:15:46
origami may someday even save a life.
00:15:50
Thanks.
00:15:52
(Applause)
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