Michael Hansmeyer: Building unimaginable shapes

185,169 views ใƒป 2012-07-27

TED


ืื ื ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ืœืžื˜ื” ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ.

00:00
Translator: Morton Bast Reviewer: Thu-Huong Ha
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ืžืชืจื’ื: Yubal Masalker ืžื‘ืงืจ: Zeeva Livshitz
00:15
As an architect, I often ask myself,
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ื›ืื“ืจื™ื›ืœ, ืœืขืชื™ื ืงืจื•ื‘ื•ืช ืื ื™ ืฉื•ืืœ ืืช ืขืฆืžื™,
00:18
what is the origin of the forms that we design?
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ืžื” ืžืงื•ืจืŸ ืฉืœ ื”ืฆื•ืจื•ืช ืฉืื ื• ืžืขืฆื‘ื™ื?
00:21
What kind of forms could we design
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ืื™ื–ื” ืกื•ื’ ืฉืœ ืฆื•ืจื•ืช ื”ื™ื™ื ื• ื™ื›ื•ืœื™ื ืœืขืฆื‘
00:23
if we wouldn't work with references anymore?
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ืื ื”ื™ื™ื ื• ืขื•ื‘ื“ื™ื ื‘ืื•ืคืŸ ืขืฆืžืื™ ืœื—ืœื•ื˜ื™ืŸ?
00:26
If we had no bias, if we had no preconceptions,
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ืื ืœื ื”ื™ืชื” ืœื ื• ืฉื•ื ื”ื˜ื™ื”, ืื ืœื ื”ื™ื• ืœื ื• ื”ื ื—ื•ืช ื™ืกื•ื“,
00:30
what kind of forms could we design
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ืื™ื–ื” ืกื•ื’ ืฉืœ ืฆื•ืจื•ืช ื ื™ืชืŸ ืœืขืฆื‘
00:32
if we could free ourselves from
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ืื ื”ื™ื™ื ื• ื™ื›ื•ืœื™ื ืœื”ืฉืชื—ืจืจ
00:33
our experience?
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ืžื”ื ื™ืกื™ื•ืŸ ืฉืœื ื•?
00:36
If we could free ourselves from our education?
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ืื ื”ื™ื™ื ื• ื™ื›ื•ืœ ืœื”ืฉืชื—ืจืจ ืžืžื” ืฉืœืžื“ื ื•?
00:40
What would these unseen forms look like?
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ืื™ืš ื”ืฆื•ืจื•ืช ื”ื ืขืœืžื•ืช ื”ืœืœื• ื”ื™ื• ื ืจืื•ืช?
00:43
Would they surprise us? Would they intrigue us?
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ื”ืื ื”ืŸ ื™ืคืชื™ืขื• ืื•ืชื ื•? ื”ืื ื”ืŸ ื™ืขื•ืจืจื• ืขื ื™ื™ืŸ?
00:47
Would they delight us?
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ื”ืื ื”ืŸ ื™ืขื ื’ื• ืื•ืชื ื•?
00:49
If so, then how can we go about creating something that is truly new?
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ืื ื›ืŸ, ืื– ืื™ืš ืื ื• ื™ื›ื•ืœื™ื ืœืœื›ืช ืขืœ ื™ืฆื™ืจืช ืžืฉื”ื• ืฉื”ื•ื ื‘ืืžืช ื—ื“ืฉ?
00:53
I propose we look to nature.
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ืื ื™ ืžืฆื™ืข ืฉื ืกืชื›ืœ ืขืœ ื”ื˜ื‘ืข.
00:56
Nature has been called the greatest architect of forms.
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ื ื”ื•ื’ ืœื•ืžืจ ืฉื”ื˜ื‘ืข ื”ื•ื ื”ืื“ืจื™ื›ืœ ื”ื’ื“ื•ืœ ืฉืœ ืฆื•ืจื•ืช.
01:00
And I'm not saying that we should copy nature,
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ืื ื™ ืœื ืื•ืžืจ ืฉืื ื—ื ื• ืฆืจื™ื›ื™ื ืœื”ืขืชื™ืง ืžื”ื˜ื‘ืข,
01:04
I'm not saying we should mimic biology,
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ืื ื™ ืœื ืื•ืžืจ ืฉืื ื—ื ื• ืฆืจื™ื›ื™ื ืœื—ืงื•ืช ืืช ื”ื‘ื™ื•ืœื•ื’ื™ื”,
01:06
instead I propose that we can borrow nature's processes.
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ื‘ืžืงื•ื ื–ื” ืื ื™ ืžืฆื™ืข ืฉื ื™ืงื— ื‘ื”ืฉืืœื” ืชื”ืœื™ื›ื™ื ืฉืœ ื”ื˜ื‘ืข.
01:09
We can abstract them and to create something that is new.
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ืื ื—ื ื• ื™ื›ื•ืœื™ื ืœื”ื•ืคื›ื ืœืžื•ืคืฉื˜ื™ื ื•ืœื™ืฆื•ืจ ืžืฉื”ื• ืฉื”ื•ื ื—ื“ืฉ.
01:14
Nature's main process of creation, morphogenesis,
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ื”ืชื”ืœื™ืš ื”ืขื™ืงืจื™ ื‘ื˜ื‘ืข ืฉื–ื” ื™ืฆื™ืจื”, ืžืชืŸ ืฆื•ืจื”,
01:18
is the splitting of one cell into two cells.
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ืžืชืจื—ืฉ ื‘ืคื™ืฆื•ืœ ืฉืœ ืชื ืื—ื“ ืœืฉื ื™ ืชืื™ื.
01:22
And these cells can either be identical,
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ืชืื™ื ืืœื” ื™ื›ื•ืœื™ื ืœื”ื™ื•ืช ื–ื”ื™ื,
01:24
or they can be distinct from each other
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ืื• ืฉื”ื ื™ื›ื•ืœื™ื ืœื”ื™ื•ืช ืฉื•ื ื™ื ื–ื” ืžื–ื”
01:26
through asymmetric cell division.
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ื‘ื’ืœืœ ื—ืœื•ืงืช ืชื ืืกื™ืžื˜ืจื™ืช.
01:28
If we abstract this process, and simplify it as much as possible,
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ืื ื ื”ืคื•ืš ืชื”ืœื™ืš ื–ื” ืœืžื•ืคืฉื˜ ื•ื‘ื ื•ืกืฃ ื’ื ื ืคืฉื˜ ืื•ืชื• ื›ื›ืœ ื”ืืคืฉืจ,
01:32
then we could start with a single sheet of paper,
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ืื– ืื ื• ื™ื›ื•ืœื™ื ืœื”ืชื—ื™ืœ ืขื ื’ื™ืœื™ื•ืŸ ื ื™ื™ืจ ื‘ื•ื“ื“,
01:34
one surface, and we could make a fold
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ืžืฉื˜ื— ืื—ื“, ื•ืื ื—ื ื• ื™ื›ื•ืœื™ื ืœืขืฉื•ืช ืงืคืœ
01:36
and divide the surface into two surfaces.
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ื•ืœื—ืœืง ืืช ื”ืžืฉื˜ื— ืœืฉื ื™ ืžืฉื˜ื—ื™ื.
01:39
We're free to choose where we make the fold.
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ืื ื—ื ื• ื—ื•ืคืฉื™ื™ื ืœื‘ื—ื•ืจ ื”ื™ื›ืŸ ืœืขืฉื•ืช ืืช ื”ืงืคืœ.
01:42
And by doing so, we can differentiate the surfaces.
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ื›ืš ืื ื• ื™ื›ื•ืœื™ื ืœื”ื‘ื“ื™ืœ ื‘ื™ืŸ ื”ืžืฉื˜ื—ื™ื.
01:47
Through this very simple process,
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ื‘ืืžืฆืขื•ืช ืชื”ืœื™ืš ืคืฉื•ื˜ ื–ื”,
01:48
we can create an astounding variety of forms.
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ื ื™ืชืŸ ืœื™ืฆื•ืจ ืžื’ื•ื•ืŸ ืžื“ื”ื™ื ืฉืœ ืฆื•ืจื•ืช.
01:52
Now, we can take this form and use the same process
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ื›ืขืช ืืคืฉืจ ืœืงื—ืช ืืช ื”ืฆื•ืจื” ื”ื–ื• ื•ืœื”ืฉืชืžืฉ ื‘ืื•ืชื• ื”ืชื”ืœื™ืš
01:55
to generate three-dimensional structures,
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ื›ื“ื™ ืœื™ืฆื•ืจ ืžื‘ื ื™ื ืชืœืช-ืžืžื“ื™ื™ื,
01:57
but rather than folding things by hand,
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ืื‘ืœ ื‘ืžืงื•ื ืœืงืคืœ ื™ื“ื ื™ืช,
01:59
we'll bring the structure into the computer,
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ื ืขื‘ื™ืจ ืืช ื”ืžื‘ื ื” ืœืžื—ืฉื‘
02:02
and code it as an algorithm.
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ื•ื ืงื•ื“ื“ ืื•ืชื• ื›ืืœื’ื•ืจื™ืชื.
02:05
And in doing so, we can suddenly fold anything.
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ื•ื‘ื›ืš, ื ื™ืชืŸ ื›ื‘ืจ ืœืงืคืœ ื›ืœ ื“ื‘ืจ.
02:08
We can fold a million times faster,
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ื ื™ืชืŸ ืœืงืคืœ ืคื™ ืžื™ืœื™ื•ืŸ ื™ื•ืชืจ ืžื”ืจ,
02:10
we can fold in hundreds and hundreds of variations.
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ื ื™ืชืŸ ืœืงืคืœ ื‘ืžืื•ืช ืจื‘ื•ืช ืฉืœ ื•ืจื™ืืฆื™ื•ืช.
02:13
And as we're seeking to make something three-dimensional,
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ื•ืžืื—ืจ ื•ืื ื• ืžื‘ืงืฉื™ื ืœื™ืฆื•ืจ ืžืฉื”ื• ืชืœืช ืžืžื“ื™,
02:16
we start not with a single surface, but with a volume.
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ืื ื—ื ื• ืžืชื—ื™ืœื™ื ืœื ืขื ืžืฉื˜ื— ืื—ื“, ืืœื ืขื ื ืคื—.
02:19
A simple volume, the cube.
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ืขื ืฆื•ืจื” ืคืฉื•ื˜ื” ืฉืœ ืงื•ื‘ื™ื™ื”.
02:20
If we take its surfaces and fold them
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ืื ืœื•ืงื—ื™ื ืืช ื”ืžืฉื˜ื—ื™ื ืฉืœื” ื•ืžืงืคืœื™ื ืื•ืชื
02:22
again and again and again and again,
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ืฉื•ื‘ ื•ืฉื•ื‘ ื•ืฉื•ื‘ ื•ืฉื•ื‘,
02:24
then after 16 iterations, 16 steps,
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ืื– ืœืื—ืจ 16 ืคืขื•ืœื•ืช ื”ื—ื•ื–ืจื•ืช ืขืœ ืขืฆืžืŸ, 16 ืฆืขื“ื™ื,
02:27
we end up with 400,000 surfaces and a shape that looks,
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ืื ื• ืžืกื™ื™ืžื™ื ืขื 400,000 ืคื™ืื•ืช ื•ืฆื•ืจื” ืฉื ืจืื™ืช,
02:31
for instance, like this.
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ืœืžืฉืœ, ื›ืžื• ื–ื•.
02:33
And if we change where we make the folds,
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ื•ืื ืžืฉื ื™ื ืืช ื”ืžืงื•ื ืฉืขื•ืฉื™ื ื‘ื• ืืช ื”ืงืคืœื™ื,
02:36
if we change the folding ratio,
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ืื ืžืฉื ื™ื ืืช ื™ื—ืก ื”ืงื™ืคื•ืœ,
02:37
then this cube turns into this one.
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ืื– ืงื•ื‘ื™ื” ื–ื• ื”ื•ืคื›ืช ืœื–ื”.
02:41
We can change the folding ratio again to produce this shape,
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ืื ื—ื ื• ื™ื›ื•ืœื™ื ืœืฉื ื•ืช ืืช ื™ื—ืก ื”ืงื™ืคื•ืœ ืฉื•ื‘ ื›ื“ื™ ืœื™ืฆื•ืจ ืืช ื”ืฆื•ืจื” ื”ื–ื•,
02:45
or this shape.
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ืื• ืฆื•ืจื” ื–ื•.
02:47
So we exert control over the form
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ื›ืš ืื ื• ืฉื•ืœื˜ื™ื ืขืœ ื”ืฆื•ืจื”
02:49
by specifying the position of where we're making the fold,
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ืขืœ ื™ื“ื™ ืฆื™ื•ืŸ ื”ืžื™ืงื•ื ืฉืœ ื™ืฆื™ืจืช ื”ืงื™ืคื•ืœ,
02:52
but essentially you're looking at a folded cube.
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ืื‘ืœ ื‘ืขืฆื ืžืกืชื›ืœื™ื ืขืœ ืงื•ื‘ื™ื™ื” ืžืงื•ืคืœืช.
02:57
And we can play with this.
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ื•ื ื™ืชืŸ ืœืฉื—ืง ืขื ื–ื”.
02:58
We can apply different folding ratios to different parts
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ื ื™ืชืŸ ืœื™ื™ืฉื ื™ื—ืกื™ ืงื™ืคื•ืœ ืฉื•ื ื™ื ืœื—ืœืงื™ื ื”ืฉื•ื ื™ื
03:00
of the form to create local conditions.
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ืฉืœ ื”ืฆื•ืจื” ื›ื“ื™ ืœื™ืฆื•ืจ ืชื ืื™ื ืžืงื•ืžื™ื™ื.
03:03
We can begin to sculpt the form.
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ืื ื—ื ื• ื™ื›ื•ืœื™ื ืœื”ืชื—ื™ืœ ืœืคืกืœ ืืช ื”ืฆื•ืจื”.
03:05
And because we're doing the folding on the computer,
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ื•ื‘ื’ืœืœ ืฉืขื•ืฉื™ื ืงื™ืคื•ืœ ื‘ืžื—ืฉื‘,
03:08
we are completely free of any physical constraints.
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ืื ื—ื ื• ื—ื•ืคืฉื™ื™ื ืœื—ืœื•ื˜ื™ืŸ ืžื›ืœ ืžื’ื‘ืœื” ืคื™ื–ื™ืช.
03:12
So that means that surfaces can intersect themselves,
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ื–ื” ืื•ืžืจ ืฉืžืฉื˜ื—ื™ื ื™ื›ื•ืœื™ื ืœื”ืฆื˜ืœื‘ ืขื ืขืฆืžื,
03:15
they can become impossibly small.
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ื”ื ื™ื›ื•ืœื™ื ืœื”ื™ื•ืช ืงื˜ื ื™ื ืœื”ื“ื”ื™ื.
03:16
We can make folds that we otherwise could not make.
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ื ื™ืชืŸ ืœื™ืฆื•ืจ ืงืคืœื™ื ืฉื‘ืžืฆื‘ ืื—ืจ ืœื ื ื™ืชืŸ ืœื™ืฆื•ืจ.
03:20
Surfaces can become porous.
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ืžืฉื˜ื—ื™ื ื™ื›ื•ืœื™ื ืœื”ื™ื•ืช ื ืงื‘ื•ื‘ื™ื™ื.
03:22
They can stretch. They can tear.
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ื”ื ื™ื›ื•ืœื™ื ืœื”ื™ืžืชื—. ื”ื ื™ื›ื•ืœื™ื ืœื”ื™ืงืจืข.
03:24
And all of this expounds the scope of forms that we can produce.
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ื•ื›ืœ ื–ื” ืžืžื—ื™ืฉ ืืช ืžื’ื•ื•ืŸ ื”ืฆื•ืจื•ืช ื”ืจื—ื‘ ืฉื ื™ืชืŸ ืœื™ืฆื•ืจ.
03:29
But in each case, I didn't design the form.
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ืื‘ืœ ื‘ื›ืœ ืžืงืจื” ืœื›ืฉืขืฆืžื•, ืœื ืขื™ืฆื‘ืชื™ ืืช ื”ืฆื•ืจื”.
03:32
I designed the process that generated the form.
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ืื ื™ ืขื™ืฆื‘ืชื™ ืืช ื”ืชื”ืœื™ืš ืฉื™ืฆืจ ืืช ื”ืฆื•ืจื”.
03:36
In general, if we make a small change to the folding ratio,
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ื‘ืื•ืคืŸ ื›ืœืœื™, ืื ืขื•ืฉื™ื ืฉื™ื ื•ื™ ืงื˜ืŸ ื‘ื™ื—ืก ื”ืงื™ืคื•ืœ,
03:41
which is what you're seeing here,
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ืฉื–ื” ืžื” ืฉืจื•ืื™ื ื›ืืŸ,
03:42
then the form changes correspondingly.
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ืื– ื”ืฆื•ืจื” ืžืฉืชื ื” ื‘ื”ืชืื.
03:46
But that's only half of the story --
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ืื‘ืœ ื–ื” ืจืง ื—ืฆื™ ืžื”ืกื™ืคื•ืจ --
03:48
99.9 percent of the folding ratios produce not this,
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99.9 ืื—ื•ื–ื™ื ืžื™ื—ืกื™ ื”ืงื™ืคื•ืœ ืœื ื™ื•ืฆืจื™ื ืืช ื–ื”,
03:53
but this, the geometric equivalent of noise.
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ืืœื ื–ื”, ืฉื•ื•ื”-ื”ืขืจืš ื”ื’ื™ืื•ืžื˜ืจื™ ืฉืœ ืจืขืฉ.
03:58
The forms that I showed before were made actually
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ื”ืฆื•ืจื•ืช ืฉื”ืจืื™ืชื™ ืงื•ื“ื, ื ืขืฉื• ื‘ืคื•ืขืœ ื‘ืืžืฆืขื•ืช
04:00
through very long trial and error.
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ืชื”ืœื™ื›ื™ ื ื™ืกื•ื™-ื•ื˜ืขื™ื™ื” ืืจื•ื›ื™ื ืžืื•ื“.
04:01
A far more effective way to create forms, I have found,
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ื“ืจืš ื™ืขื™ืœื” ื”ืจื‘ื” ื™ื•ืชืจ ืฉื’ื™ืœื™ืชื™ ืœื™ืฆื™ืจืช ืฆื•ืจื•ืช
04:05
is to use information that is already contained in forms.
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ื”ื™ื ืœื”ืฉืชืžืฉ ื‘ืžื™ื“ืข ืฉื›ื‘ืจ ื›ืœื•ืœ ื‘ืฆื•ืจื•ืช.
04:09
A very simple form such as this one actually contains
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ืฆื•ืจื” ืžืื•ื“ ืคืฉื•ื˜ื” ื›ื’ื•ืŸ ื–ื• ืžื›ื™ืœื” ืœืžืขืฉื”
04:11
a lot of information that may not be visible to the human eye.
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ืžื™ื“ืข ืจื‘ ืฉืขืฉื•ื™ ืœื”ื™ื•ืช ื ืกืชืจ ืžืขื™ืŸ ืื ื•ืฉื™ืช.
04:15
So, for instance, we can plot the length of the edges.
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ื›ืš, ืœืžืฉืœ, ื ื•ื›ืœ ืœืฉืจื˜ื˜ ืืช ืื•ืจืš ื”ืงืฆื•ื•ืช.
04:17
White surfaces have long edges, black ones have short ones.
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ืœืžืฉื˜ื—ื™ื ืœื‘ื ื™ื ื™ืฉ ืงืฆื•ื•ืช ืืจื•ื›ื™ื, ืœืฉื—ื•ืจื™ื ืงืฆืจื™ื.
04:21
We can plot the planarity of the surfaces, their curvature,
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ื ื•ื›ืœ ืœืฉืจื˜ื˜ ืืช ื”ืžื™ืฉื•ืจื™ื•ืช ืฉืœ ื”ืžืฉื˜ื—ื™ื, ืืช ืขืงืžื•ืžื™ื•ืชื,
04:24
how radial they are -- all information that may not be
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ืขื“ ื›ืžื” ื”ื ืžืžื•ืจื›ื–ื™ื -- ื›ืœ ื”ืžื™ื“ืข ืฉื™ื™ืชื›ืŸ ื•ืœื ื™ื”ื™ื”
04:28
instantly visible to you,
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ื’ืœื•ื™ ืœืขื™ื ื™ื ื•,
04:30
but that we can bring out, that we can articulate,
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ืื‘ืœ ืฉืื ื• ื™ื›ื•ืœื™ื ืœื—ืฉื•ืฃ,
04:33
and that we can use to control the folding.
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ืฉืื ื• ื™ื›ื•ืœื™ื ืœื‘ื˜ื, ื•ืฉื™ื›ื•ืœื™ื ืœื”ืฉืชืžืฉ ื‘ื• ื›ื“ื™ ืœืฉืœื•ื˜ ื‘ืงื™ืคื•ืœ.
04:36
So now I'm not specifying a single
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ืขื›ืฉื™ื• ืื ื™ ืœื ืงื•ื‘ืข ื™ื•ืชืจ
04:38
ratio anymore to fold it,
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ื™ื—ืก ืื—ื“ ื•ื™ื—ื™ื“ ื›ื“ื™ ืœืงืคืœ ืื•ืชื”,
04:40
but instead I'm establishing a rule,
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ืืœื ื‘ืžืงื•ื ื–ื” ืื ื™ ื™ื•ืฆืจ ื›ืœืœ.
04:43
I'm establishing a link between a property of a surface
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ืื ื™ ื™ื•ืฆืจ ืงืฉืจ ื‘ื™ืŸ ืชื›ื•ื ื” ืฉืœ ืžืฉื˜ื—
04:45
and how that surface is folded.
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ื•ืื™ืš ืฉื”ืžืฉื˜ื— ืžืงื•ืคืœ.
04:48
And because I've designed the process and not the form,
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ื•ืžื›ื™ื•ื•ืŸ ืฉืื ื™ ืขื™ืฆื‘ืชื™ ืืช ื”ืชื”ืœื™ืš ื•ืœื ืืช ื”ืฆื•ืจื”,
04:51
I can run the process again and again and again
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ืื ื™ ื™ื›ื•ืœ ืœื”ืคืขื™ืœ ืืช ื”ืชื”ืœื™ืš ืฉื•ื‘ ื•ืฉื•ื‘ ื•ืฉื•ื‘
04:53
to produce a whole family of forms.
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ื›ื“ื™ ืœื™ืฆื•ืจ ืžืฉืคื—ื” ืฉืœืžื” ืฉืœ ืฆื•ืจื•ืช.
05:08
These forms look elaborate, but the process is a very minimal one.
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ืฆื•ืจื•ืช ืืœื• ื ืจืื•ืช ืžืฉื•ื›ืœืœื•ืช, ืื‘ืœ ื”ืชื”ืœื™ืš ื”ื•ื ืžืื•ื“ ืคืฉื•ื˜.
05:13
There is a simple input,
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ื™ืฉ ืงืœื˜ ืคืฉื•ื˜,
05:14
it's always a cube that I start with,
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ืฉื–ื• ืชืžื™ื“ ืงื•ื‘ื™ื™ื” ืฉืื ื™ ืžืชื—ื™ืœ ื‘ื”,
05:16
and it's a very simple operation -- it's making a fold,
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ื•ื–ื• ืคืขื•ืœื” ืคืฉื•ื˜ื” ืžืื•ื“ -- ืฉื–ื” ื™ืฆื™ืจืช ืงื™ืคื•ืœ,
05:19
and doing this over and over again.
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ื•ื—ื–ืจื” ืขืœ ื›ืš ืฉื•ื‘ ื•ืฉื•ื‘.
05:23
So let's bring this process to architecture.
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ื›ืขืช ื”ื‘ื” ื ื‘ื™ื ืชื”ืœื™ืš ื–ื” ืœืขื•ืœื ื”ืื“ืจื™ื›ืœื•ืช.
05:25
How? And at what scale?
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ื›ื™ืฆื“? ื•ื‘ืื™ื–ื” ื”ื™ืงืฃ?
05:27
I chose to design a column.
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ืื ื™ ื‘ื—ืจืชื™ ืœืขืฆื‘ ืขืžื•ื“.
05:29
Columns are architectural archetypes.
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ืขืžื•ื“ื™ื ืžื”ื•ื•ื™ื ืื‘-ื˜ื™ืคื•ืก ืื“ืจื™ื›ืœื™.
05:32
They've been used throughout history to express ideals
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ื”ื ืฉื™ืžืฉื• ืœื›ืœ ืื•ืจืš ื”ื”ื™ืกื˜ื•ืจื™ื” ืœื”ื‘ื™ืข ืื™ื“ืืœื™ื
05:35
about beauty, about technology.
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ืฉืœ ื™ื•ืคื™, ืฉืœ ื˜ื›ื ื•ืœื•ื’ื™ื”.
05:40
A challenge to me was how we could express
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ื”ืืชื’ืจ ืžื‘ื—ื™ื ืชื™ ื”ื™ื” ื›ื™ืฆื“ ืœื‘ื˜ื
05:42
this new algorithmic order in a column.
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ื—ื•ืงื™ื•ืช ืืœื’ื•ืจื™ืชืžื™ืช ื—ื“ืฉื” ื–ื• ื‘ืขืžื•ื“.
05:46
I started using four cylinders.
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ื”ืชื—ืœืชื™ ืขื ืืจื‘ืขื” ื’ืœื™ืœื™ื.
05:49
Through a lot of experimentation, these cylinders
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ืœืื—ืจ ื ื™ืกื•ื™ื™ื ืจื‘ื™ื, ื”ื’ืœื™ืœื™ื ื”ืืœื”
05:52
eventually evolved into this.
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ื”ืชืคืชื—ื• ืœื“ื‘ืจ ื›ื–ื”.
05:55
And these columns, they have information at very many scales.
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ื•ืขืžื•ื“ื™ื ืืœื”, ื™ืฉ ื‘ืงืจื‘ื ืžื™ื“ืข ื‘ืงื ื™-ืžื™ื“ื” ืฉื•ื ื™ื.
06:00
We can begin to zoom into them.
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ืืคืฉืจ ืœื”ืชื—ื™ืœ ืœื”ืชืงืจื‘ ืืœื™ื”ื.
06:03
The closer one gets, the more new features one discovers.
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ื›ื›ืœ ืฉืžืชืงืจื‘ื™ื, ื›ืš ืžืชื’ืœื•ืช ืชื›ื•ื ื•ืช ื—ื“ืฉื•ืช.
06:06
Some formations are almost at the threshold of human visibility.
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ืชืฆื•ืจื•ืช ืžืกื•ื™ืžื•ืช ื”ืŸ ื›ืžืขื˜ ืขืœ ืกืฃ ื™ื›ื•ืœืช ื”ืจืื™ื” ื”ืื ื•ืฉื™ืช.
06:10
And unlike traditional architecture,
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ื•ื‘ื ื™ื’ื•ื“ ืœืืจื›ื™ื˜ืงื˜ื•ืจื” ื”ืžืกื•ืจืชื™ืช,
06:12
it's a single process that creates both the overall form
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ื–ื”ื• ืชื”ืœื™ืš ืื—ื“ ืฉื™ื•ืฆืจ ื”ืŸ ืืช
06:15
and the microscopic surface detail.
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ื”ืฆื•ืจื” ื”ื›ืœืœื™ืช ื•ื”ืŸ ืืช ืคืจื˜ื™ ื”ืžืฉื˜ื— ื”ืžื™ืงืจื•ืกืงื•ืคื™ื™ื.
06:20
These forms are undrawable.
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ืœื ื ื™ืชืŸ ืœืฉืจื˜ื˜ ืฆื•ืจื•ืช ืืœื• ื‘ืื•ืคืŸ ื™ื“ื ื™.
06:23
An architect who's drawing them with a pen and a paper
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ืื“ืจื™ื›ืœ ืฉื™ืฉืจื˜ื˜ ืื•ืชื ืขื ืขื˜ ื•ื ื™ื™ืจ,
06:26
would probably take months,
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ื™ืงื— ืœื• ืงืจื•ื‘ ืœื•ื•ื“ืื™ ื—ื•ื“ืฉื™ื,
06:28
or it would take even a year to draw all the sections,
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ืื• ืื•ืœื™ ืืคื™ืœื• ืฉื ื” ื›ื“ื™ ืœืฉืจื˜ื˜ ืืช ื›ืœ ื”ื—ืœืงื™ื,
06:30
all of the elevations, you can only create something like this
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ื›ืœ ื”ื’ื‘ื”ื™ื -- ื ื™ืชืŸ ืœื™ืฆื•ืจ ืžืฉื”ื• ื›ื–ื”
06:32
through an algorithm.
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ืจืง ื‘ืืžืฆืขื•ืช ืืœื’ื•ืจื™ืชื.
06:35
The more interesting question, perhaps, is,
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ืื•ืœื™ ื”ืฉืืœื” ื”ืžืขื ื™ื™ื ืช ื™ื•ืชืจ ื”ื™ื,
06:37
are these forms imaginable?
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ื”ืื ื ื™ืชืŸ ืœื”ืขืœื•ืช ืขืœ ื”ื“ืขืช ืฆื•ืจื•ืช ื›ืืœื•?
06:39
Usually, an architect can somehow envision the end state
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ื‘ื“ืจืš ื›ืœืœ, ืื“ืจื™ื›ืœ ื™ื›ื•ืœ ืื™ื›ืฉื”ื• ืœื“ืžื™ื™ืŸ
06:42
of what he is designing.
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ืืช ื”ืžืฆื‘ ื”ืกื•ืคื™ ืฉืœ ืžื” ืฉื”ื•ื ืžืขืฆื‘.
06:44
In this case, the process is deterministic.
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ื‘ืžืงืจื” ื”ื–ื”, ื”ืชื”ืœื™ืš ื”ื•ื ื“ื˜ืจืžื™ื ื™ืกื˜ื™.
06:47
There's no randomness involved at all,
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ื”ืืงืจืื™ื•ืช ืื™ื ื” ืžืขื•ืจื‘ืช ื›ืืŸ ื›ืœืœ,
06:49
but it's not entirely predictable.
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ืื‘ืœ ื–ื” ืœื ืœื—ืœื•ื˜ื™ืŸ ื ื™ืชืŸ ืœื—ื™ื–ื•ื™.
06:51
There's too many surfaces,
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ื™ืฉ ื™ื•ืชืจ ืžื“ื™ ืžืฉื˜ื—ื™ื,
06:52
there's too much detail, one can't see the end state.
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ื™ืฉ ื™ื•ืชืจ ืžื“ื™ ืคืจื˜ื™ื, ืœื ื ื™ืชืŸ ืœืจืื•ืช ืืช ื”ืžืฆื‘ ื”ืกื•ืคื™.
06:56
So this leads to a new role for the architect.
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ืœื›ืŸ ื–ื” ืžื•ื‘ื™ืœ ืœืชืคืงื™ื“ ื—ื“ืฉ ืฉืœ ื”ืื“ืจื™ื›ืœ.
06:59
One needs a new method to explore all of the possibilities
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ื™ืฉ ืฆื•ืจืš ื‘ืฉื™ื˜ื” ื—ื“ืฉื” ืœื’ืœื•ืช ืืช ื›ืœ ื”ืืคืฉืจื•ื™ื•ืช
07:03
that are out there.
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ื”ืงื™ื™ืžื•ืช ื‘ืคื•ืขืœ.
07:05
For one thing, one can design many variants of a form,
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ืงื•ื“ื ื›ืœ, ืืคืฉืจ ืœืชื›ื ืŸ ื”ืจื‘ื” ื’ืจืกืื•ืช ืฉืœ ืฆื•ืจื”,
07:08
in parallel, and one can cultivate them.
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ื‘ืžืงื‘ื™ืœ, ื•ืื– ืืคืฉืจ ืœืขื‘ื“ ืื•ืชืŸ.
07:10
And to go back to the analogy with nature,
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ืื ืœื—ื–ื•ืจ ืœืื ืœื•ื’ื™ื” ืขื ื”ื˜ื‘ืข,
07:12
one can begin to think in terms of populations,
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ืืคืฉืจ ืœื”ืชื—ื™ืœ ืœื—ืฉื•ื‘ ื‘ืžื•ื ื—ื™ื ืฉืœ ืื•ื›ืœื•ืกื™ื•ืช,
07:15
one can talk about permutations, about generations,
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ืืคืฉืจ ืœื“ื‘ืจ ืขืœ ืชืžื•ืจื•ืช, ืขืœ ื“ื•ืจื•ืช,
07:18
about crossing and breeding to come up with a design.
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ืขืœ ื”ืฆื˜ืœื‘ื•ื™ื•ืช ื•ืจื‘ื™ื™ื”, ืขื“ ืฉืžืชืงื‘ืœ ื”ืขื™ืฆื•ื‘ ื”ืกื•ืคื™.
07:23
And the architect is really, he moves into the position
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ื•ื”ืื“ืจื™ื›ืœ ื”ื•ื ื‘ืืžืช -- ื”ื•ื ืขื•ื‘ืจ ืœืžืฆื‘
07:26
of being an orchestrator of all of these processes.
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ืฉืœ ืœื”ื™ื•ืช ื”ืžื ืฆื— ืขืœ ื”ืชื”ืœื™ื›ื™ื ื”ืœืœื•.
07:29
But enough of the theory.
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ืื‘ืœ ื“ื™ ืœื“ื‘ืจ ื‘ืชืื•ืจื™ื”.
07:31
At one point I simply wanted to jump inside
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ื‘ืฉืœื‘ ืžืกื•ื™ื ืคืฉื•ื˜ ืจืฆื™ืชื™ ืœืงืคื•ืฅ ืคื ื™ืžื”
07:34
this image, so to say, I bought these red and blue
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ืœืชื•ืš ืชืžื•ื ื” ื–ื•, ืœื›ืŸ ืงื ื™ืชื™ ืžืฉืงืคื™ ืชืœืช-ืžื™ืžื“ ืื“ื•ื-ื›ื—ื•ืœ
07:38
3D glasses, got up very close to the screen,
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ืืœื”, ื”ืชืงืจื‘ืชื™ ืžืื•ื“ ืœืžืกืš,
07:41
but still that wasn't the same as being able to
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ืื‘ืœ ืขื“ื™ื™ืŸ ื–ื” ืœื ื”ื™ื” ื›ืžื• ืœื”ื™ื•ืช ืžืกื•ื’ืœ
07:43
walk around and touch things.
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ืœื”ืชื”ืœืš ื•ืœื’ืขืช ื‘ื“ื‘ืจื™ื.
07:45
So there was only one possibility --
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ืื– ื ืฉืืจื” ืจืง ืืคืฉืจื•ืช ืื—ืช --
07:47
to bring the column out of the computer.
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ืœื”ื‘ื™ื ืืช ื”ืขืžื•ื“ ืืœ ืžื—ื•ืฅ ืœืžื—ืฉื‘.
07:50
There's been a lot of talk now about 3D printing.
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ื™ืฉ ื”ืจื‘ื” ื“ื™ื‘ื•ืจื™ื ืขื›ืฉื™ื• ืขืœ ื”ื“ืคืกืช ืชืœืช-ืžื™ืžื“.
07:53
For me, or for my purpose at this moment,
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ื‘ืฉื‘ื™ืœื™, ืื• ืœืžื˜ืจื” ืฉืœื™ ื‘ืจื’ืข ื–ื”,
07:56
there's still too much of an unfavorable tradeoff
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ื™ืฉ ืขื“ื™ื™ืŸ ื™ื•ืชืจ ืžื“ื™ ื™ื—ืกื™-ื’ื•ืžืœื™ืŸ ื‘ืœืชื™ ืžืื•ื–ื ื™ื
07:59
between scale, on the one hand, and resolution and speed, on the other.
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ื‘ื™ืŸ ื’ื•ื“ืœ, ืžืฆื“ ืื—ื“, ื•ืจื–ื•ืœื•ืฆื™ื” ื•ืžื”ื™ืจื•ืช, ืžืฆื“ ื”ืฉื ื™.
08:06
So instead, we decided to take the column,
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ืœื›ืŸ ื‘ืžืงื•ื ื–ืืช, ื”ื—ืœื˜ื ื• ืœืงื—ืช ืืช ื”ืขืžื•ื“,
08:08
and we decided to build it as a layered model,
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ื•ื”ื—ืœื˜ื ื• ืœื‘ื ื•ืช ืื•ืชื• ื›ืžื•ื“ืœ ืฉื›ื‘ืชื™,
08:11
made out of very many slices, thinly stacked over each other.
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ืขืฉื•ื™ ืžืคืจื•ืกื•ืช ืจื‘ื•ืช ืžืื•ื“, ื ืขืจืžื•ืช ื“ืง ืื—ืช ืขืœ ืฉื ื™ื™ื”.
08:15
What you're looking at here is an X-ray
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ืžื” ืฉืจื•ืื™ื ื›ืืŸ ื”ื•ื ืฆื™ืœื•ื ืจื ื˜ื’ืŸ
08:17
of the column that you just saw, viewed from the top.
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ืฉืœ ื”ืขืžื•ื“ ืฉื›ืจื’ืข ืจืื™ื ื•, ื‘ืžื‘ื˜ ืžืœืžืขืœื”.
08:19
Unbeknownst to me at the time,
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ื‘ืœื-ื™ื•ื“ืขื™ืŸ ื‘ืื•ืชื” ื”ืขืช,
08:21
because we had only seen the outside,
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ื‘ื’ืœืœ ืฉืจืื™ื ื• ืจืง ืžื‘ื—ื•ืฅ,
08:24
the surfaces were continuing to fold themselves,
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ื”ืžืฉื˜ื—ื™ื ื”ื™ื• ืžืžืฉื™ื›ื™ื ืœืงืคืœ ืืช ืขืฆืžื,
08:26
to grow on the inside of the column,
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ืœื’ื“ื•ืœ ื‘ื—ืœืง ื”ืคื ื™ืžื™ ืฉืœ ื”ืขืžื•ื“,
08:28
which was quite a surprising discovery.
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ื“ื‘ืจ ืฉื”ื™ื” ืชื’ืœื™ืช ืžืคืชื™ืขื” ืœืžื“ื™.
08:31
From this shape, we calculated a cutting line,
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ืžืฆื•ืจื” ื–ื•, ื—ื™ืฉื‘ื ื• ืงื• ื—ื™ืชื•ืš,
08:34
and then we gave this cutting line to a laser cutter
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ื•ืื– ืฉืžื ื• ืงื• ื—ื™ืชื•ืš ื–ื” ืชื—ืช ื—ื•ืชืš ืœื™ื™ื–ืจ
08:37
to produce -- and you're seeing a segment of it here --
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ื›ื“ื™ ืœื™ืฆื•ืจ -- ื•ืจื•ืื™ื ื›ืืŸ ืงื˜ืข ืžืžื ื• --
08:41
very many thin slices, individually cut, on top of each other.
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ื”ืจื‘ื” ืžืื•ื“ ืคืจื•ืกื•ืช ื“ืงื•ืช, ื—ืชื•ื›ื•ืช ื›ืœ ืื—ืช ื‘ื ืคืจื“, ืžื•ื ื—ื•ืช ืื—ืช ืขืœ ื’ื‘ื™ ื”ืฉื ื™ื”.
08:48
And this is a photo now, it's not a rendering,
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ื›ืืŸ ื–ื• ืชืžื•ื ื”, ื–ื• ืœื ื”ื“ืžื™ื”.
08:51
and the column that we ended up with
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ื”ืขืžื•ื“ ืฉื”ื’ืขื ื• ืืœื™ื• ื‘ืกื•ืฃ
08:53
after a lot of work, ended up looking remarkably like the one
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ืื—ืจื™ ืขื‘ื•ื“ื” ืจื‘ื”, ื ืจืื” ื‘ืžื™ื“ื” ืจื‘ื”
08:56
that we had designed in the computer.
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ื›ืžื• ื–ื” ืฉืขื™ืฆื‘ื ื• ื‘ืžื—ืฉื‘.
09:00
Almost all of the details, almost all of the
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ื›ืžืขื˜ ื›ืœ ื”ืคืจื˜ื™ื, ื›ืžืขื˜ ื›ืœ
09:02
surface intricacies were preserved.
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ืžื•ืจื›ื‘ื•ื™ื•ืช ื”ืฉื˜ื—, ื”ืฉืชืžืจื•.
09:07
But it was very labor intensive.
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ืื‘ืœ ื–ื” ื”ื™ื” ืœืื—ืจ ืขื‘ื•ื“ื” ืžืื•ื“ ืื™ื ื˜ื ืกื™ื‘ื™ืช.
09:10
There's a huge disconnect at the moment still
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ื™ืฉ ืขื“ื™ื™ืŸ ืžืจื—ืง ื’ื“ื•ืœ ืžืื•ื“
09:12
between the virtual and the physical.
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ื‘ื™ืŸ ื”ื•ื•ื™ืจื˜ื•ืืœื™ ืœืคื™ื–ื™.
09:15
It took me several months to design the column,
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ืœืงื— ืœื™ ื›ืžื” ื—ื•ื“ืฉื™ื ืœืชื›ื ืŸ ืืช ื”ืขืžื•ื“,
09:17
but ultimately it takes the computer about 30 seconds
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ืื‘ืœ ื‘ืกื•ืคื• ืฉืœ ื“ื‘ืจ ืœื•ืงื— ืœืžื—ืฉื‘ ื›-30 ืฉื ื™ื•ืช
09:20
to calculate all of the 16 million faces.
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ื›ื“ื™ ืœื—ืฉื‘ ืืช ื›ืœ 16 ืžื™ืœื™ื•ืŸ ื”ืคื™ืื•ืช.
09:23
The physical model, on the other hand,
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ื”ืžื•ื“ืœ ื”ืคื™ื–ื™, ืžืฆื“ ื”ืฉื ื™,
09:25
is 2,700 layers, one millimeter thick,
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ื”ื•ื ื‘ืขืœ 2,700 ืฉื›ื‘ื•ืช, ื‘ืขื•ื‘ื™ ืžื™ืœื™ืžื˜ืจ ืื—ื“,
09:29
it weighs 700 kilos, it's made of sheet that can cover
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ื”ื•ื ืฉื•ืงืœ 700 ืง"ื’ ื•ื”ื•ื ืขืฉื•ื™ ืžื™ืจื™ืขื” ืฉื™ื›ื•ืœื” ืœื›ืกื•ืช
09:33
this entire auditorium.
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ืืช ื›ืœ ื”ืื•ืœื ื”ื–ื”.
09:35
And the cutting path that the laser followed
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ืžืกืœื•ืœ ื”ื—ื™ืชื•ืš ืฉื”ืœื™ื™ื–ืจ ืขื‘ืจ,
09:37
goes from here to the airport and back again.
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ืื•ืจื›ื• ื›ืžืจื—ืง ืžื›ืืŸ ืœื ืžืœ-ื”ืชืขื•ืคื” ื•ื‘ื—ื–ืจื”.
09:42
But it is increasingly possible.
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ืื‘ืœ ื–ื” ื™ื•ืชืจ ื•ื™ื•ืชืจ ืืคืฉืจื™ ืœื‘ื™ืฆื•ืข.
09:44
Machines are getting faster, it's getting less expensive,
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ื”ืžื›ื•ื ื•ืช ื”ื•ืคื›ื•ืช ืœืžื”ื™ืจื•ืช ื™ื•ืชืจ, ื”ืขืœื•ืช ื™ื•ืจื“ืช
09:47
and there's some promising technological developments
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ื•ื‘ืื•ืคืง ืจื•ืื™ื ื›ืžื” ื”ืชืคืชื—ื•ื™ื•ืช
09:49
just on the horizon.
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ื˜ื›ื ื•ืœื•ื’ื™ื•ืช ืžื‘ื˜ื™ื—ื•ืช.
09:51
These are images from the Gwangju Biennale.
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ืืœื• ื”ืŸ ืชืžื•ื ื•ืช ืžื”ื‘ื™ืื ืœื” ื‘ื’ื•ื•ืื ื’'ื•.
09:54
And in this case, I used ABS plastic to produce the columns,
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ื•ื‘ืžืงืจื” ื”ื–ื”, ื”ืฉืชืžืฉืชื™ ื‘ืคืœืกื˜ื™ืง ABS ื›ื“ื™ ืœื™ื™ืฆืจ ืืช ื”ืขืžื•ื“ื™ื.
09:58
we used the bigger, faster machine,
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ื”ืฉืชืžืฉื ื• ื‘ืžื›ื•ื ื” ื’ื“ื•ืœื” ื™ื•ืชืจ, ืžื”ื™ืจื” ื™ื•ืชืจ
10:00
and they have a steel core inside, so they're structural,
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ื•ื™ืฉ ืœื”ื ื‘ืคื ื™ื ืœื™ื‘ืช ืคืœื“ื” ื•ืœื›ืŸ ื”ื ืžื‘ื ื™ื™ื.
10:03
they can bear loads for once.
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ืœืฉื ืฉื™ื ื•ื™, ื”ื ื™ื›ื•ืœื™ื ืœืฉืืช ืขื•ืžืกื™ื.
10:06
Each column is effectively a hybrid of two columns.
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ื›ืœ ืขืžื•ื“ ื”ื•ื ืœืžืขืฉื” ื‘ืŸ-ื›ืœืื™ื™ื ืฉืœ ืฉื ื™ ืขืžื•ื“ื™ื.
10:08
You can see a different column in the mirror,
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ื ื™ืชืŸ ืœืจืื•ืช ืขืžื•ื“ ืฉื•ื ื” ื‘ืžืจืื”,
10:11
if there's a mirror behind the column
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ืื ื™ืฉ ืžืจืื” ืžืื—ื•ืจื™ ื”ืขืžื•ื“
10:13
that creates a sort of an optical illusion.
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ืฉื™ื•ืฆืจืช ืžืขื™ืŸ ืืฉืœื™ื” ืื•ืคื˜ื™ืช.
10:16
So where does this leave us?
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ืื– ืื™ืคื” ื–ื” ืžืฉืื™ืจ ืื•ืชื ื•?
10:18
I think this project gives us a glimpse of the unseen objects that await us
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ืื ื™ ื—ื•ืฉื‘ ืฉื”ืคืจื•ื™ื™ืงื˜ ื”ื–ื” ื ื•ืชืŸ ืœื ื• ื”ืฆืฆื” ืืœ ืขืฆืžื™ื ื‘ืœืชื™ ื ืจืื™ื ืฉืžื—ื›ื™ื ืœื ื•
10:22
if we as architects begin to think about designing not the object,
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ืื ืื ื—ื ื• ื›ืื“ืจื™ื›ืœื™ื ืžืชื—ื™ืœื™ื ืœื—ืฉื•ื‘ ืขืœ ืขื™ืฆื•ื‘, ืœื ืฉืœ ื”ืขืฆื,
10:26
but a process to generate objects.
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ืืœื ืขืœ ืขื™ืฆื•ื‘ ืฉืœ ื”ืชื”ืœื™ืš ืœื™ืฆื™ืจืช ื”ืขืฆืžื™ื.
10:30
I've shown one simple process that was inspired by nature;
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ื”ืฆื’ืชื™ ืชื”ืœื™ืš ืคืฉื•ื˜ ืฉื ื•ืฆืจ ื‘ื”ืฉืจืืชื• ืฉืœ ื”ื˜ื‘ืข;
10:33
there's countless other ones.
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ื™ืฉื ื ืื™ืŸ-ืกืคื•ืจ ืื—ืจื™ื.
10:36
In short, we have no constraints.
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ื‘ืงื™ืฆื•ืจ, ืื™ืŸ ืœื ื• ืื™ืœื•ืฆื™ื.
10:39
Instead, we have processes in our hands right now
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ื‘ืžืงื•ื ื–ืืช, ื™ืฉ ืœื ื• ืชื”ืœื™ื›ื™ื, ื‘ื™ื“ื™ื™ื ืฉืœื ื• ืžืžืฉ ืขื›ืฉื™ื•,
10:43
that allow us to create structures at all scales
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ืฉื™ืืคืฉืจื• ืœื ื• ืœื™ืฆื•ืจ ืžื‘ื ื™ื ื‘ื›ืœ ืงื ื”-ืžื™ื“ื”
10:47
that we couldn't even have dreamt up.
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ืฉืื ื—ื ื• ืืคื™ืœื• ืœื ื™ื›ื•ืœื™ื ืœื—ืœื•ื.
10:51
And, if I may add, at one point we will build them.
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ื•ื’ื, ืื ื™ื•ืจืฉื” ืœื™ ืœื”ื•ืกื™ืฃ, ื‘ืฉืœื‘ ืžืกื•ื™ื ื ื‘ื ื” ืื•ืชื.
10:55
Thank you. (Applause)
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ืชื•ื“ื”. (ืžื—ื™ืื•ืช ื›ืคื™ื™ื)
ืขืœ ืืชืจ ื–ื”

ืืชืจ ื–ื” ื™ืฆื™ื’ ื‘ืคื ื™ื›ื ืกืจื˜ื•ื ื™ YouTube ื”ืžื•ืขื™ืœื™ื ืœืœื™ืžื•ื“ ืื ื’ืœื™ืช. ืชื•ื›ืœื• ืœืจืื•ืช ืฉื™ืขื•ืจื™ ืื ื’ืœื™ืช ื”ืžื•ืขื‘ืจื™ื ืขืœ ื™ื“ื™ ืžื•ืจื™ื ืžื”ืฉื•ืจื” ื”ืจืืฉื•ื ื” ืžืจื—ื‘ื™ ื”ืขื•ืœื. ืœื—ืฅ ืคืขืžื™ื™ื ืขืœ ื”ื›ืชื•ื‘ื™ื•ืช ื‘ืื ื’ืœื™ืช ื”ืžื•ืฆื’ื•ืช ื‘ื›ืœ ื“ืฃ ื•ื™ื“ืื• ื›ื“ื™ ืœื”ืคืขื™ืœ ืืช ื”ืกืจื˜ื•ืŸ ืžืฉื. ื”ื›ืชื•ื‘ื™ื•ืช ื’ื•ืœืœื•ืช ื‘ืกื ื›ืจื•ืŸ ืขื ื”ืคืขืœืช ื”ื•ื•ื™ื“ืื•. ืื ื™ืฉ ืœืš ื”ืขืจื•ืช ืื• ื‘ืงืฉื•ืช, ืื ื ืฆื•ืจ ืื™ืชื ื• ืงืฉืจ ื‘ืืžืฆืขื•ืช ื˜ื•ืคืก ื™ืฆื™ืจืช ืงืฉืจ ื–ื”.

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