Greg Lynn: How calculus is changing architecture

68,852 views ・ 2009-01-13

TED


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00:12
What I thought I would talk about today
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is the transition from one mode
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of thinking about nature
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to another that's tracked by architecture.
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What's interesting about architects is,
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we always have tried to justify beauty
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by looking to nature,
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and arguably, beautiful architecture
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has always been looking at a model of nature.
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So, for roughly 300 years,
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the hot debate in architecture
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was whether the number five
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or the number seven
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was a better proportion to think about architecture,
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because the nose was one-fifth of your head,
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or because your head was one-seventh of your body.
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And the reason that that was the model
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of beauty and of nature
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was because the decimal point had not been invented yet --
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it wasn't the 16th century --
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and everybody had to dimension a building
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in terms of fractions,
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so a room would be dimensioned
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as one-fourth of a facade;
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the structural dais of that might be dimensioned as 10 units,
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and you would get down to the small elements
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by fractional subdivision:
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finer and finer and finer.
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In the 15th century, the decimal point was invented;
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architects stopped using fractions,
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and they had a new model of nature.
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So, what's going on today
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is that there's a model of natural form
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which is calculus-based
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and which is using digital tools,
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and that has a lot of implications
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to the way we think about beauty and form,
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and it has a lot of implications in the way we think about nature.
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The best example of this would probably be the Gothic,
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and the Gothic was invented after the invention of calculus,
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although the Gothic architects
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weren't really using calculus to define their forms.
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But what was important is,
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the Gothic moment in architecture was the first time
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that force and motion was thought of in terms of form.
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So, examples like Christopher Wren's King's Cross:
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you can see that the structural forces of the vaulting
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get articulated as lines, so you're really actually seeing
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the expression of structural force and form.
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Much later, Robert Maillart's bridges,
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which optimize structural form
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with a calculus curvature almost like a parabola.
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The Hanging Chain models of Antonio Gaudi,
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the Catalan architect.
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The end of the 19th century, beginning of the 20th century,
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and how that Hanging Chain model
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translates into archways
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and vaulting.
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So, in all of these examples,
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structure is the determining force.
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Frei Otto was starting to use foam bubble diagrams
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and foam bubble models to generate his Mannheim Concert Hall.
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Interestingly, in the last 10 years
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Norman Foster used a similar heat thermal transfer model
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to generate the roof of the National Gallery,
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with the structural engineer Chris Williams.
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In all these examples,
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there's one ideal form,
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because these are thought in terms of structure.
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And as an architect, I've always found these kinds of systems
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very limiting, because I'm not interested in ideal forms
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and I'm not interested in optimizing to some perfect moment.
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So, what I thought I would bring up is
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another component that needs to be thought of,
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whenever you think about nature,
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and that's basically the invention of
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generic form in genetic evolution.
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My hero is actually not Darwin;
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it's a guy named William Bateson,
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father of Greg Bateson, who was here for a long time in Monterey.
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And he was what you'd call a teratologist:
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he looked at all of the monstrosities and mutations
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to find rules and laws, rather than looking at the norms.
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So, instead of trying to find the ideal type
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or the ideal average,
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he'd always look for the exception. So, in this example,
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which is an example of what's called Bateson's Rule,
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he has two kinds of mutations of a human thumb.
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When I first saw this image, 10 years ago,
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I actually found it very strange and beautiful at the same time.
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Beautiful, because it has symmetry.
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So, what he found is that in all cases of thumb mutations,
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instead of having a thumb,
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you would either get another opposable thumb,
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or you would get four fingers.
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So, the mutations reverted to symmetry.
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And Bateson invented
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the concept of symmetry breaking,
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which is that
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wherever you lose information in a system,
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you revert back to symmetry.
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So, symmetry wasn't the sign of order and organization --
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which is what I was always understanding, and as is an architect --
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symmetry was the absence of information.
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So, whenever you lost information, you'd move to symmetry;
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whenever you added information to a system, you would break symmetry.
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So, this whole idea of natural form shifted at that moment
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from looking for ideal shapes
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to looking for a combination of
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information and generic form.
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You know, literally after seeing that image,
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and finding out what Bateson was working with,
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we started to use these rules for symmetry breaking and branching
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to start to think about architectural form.
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To just talk for a minute about the
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digital mediums that we're using now
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and how they integrate calculus:
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the fact that they're calculus-based
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means that we don't have to think about dimension
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in terms of ideal units
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or discreet elements.
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So, in architecture we deal with
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big assemblies of components,
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so there might be up to, say,
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50,000 pieces of material
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in this room you're sitting in right now
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that all need to get organized.
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Now, typically you'd think that they would all be the same:
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like, the chairs you're sitting in would all be the same dimension.
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You know, I haven't verified this, but it's the norm
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that every chair would be a slightly different dimension,
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because you'd want to space them all out for everybody's sight lines.
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The elements that make up the ceiling grid and the lighting,
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they're all losing their modular quality,
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and moving more and more to these infinitesimal dimensions.
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That's because we're all using calculus tools
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for manufacturing and for design.
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Calculus is also a mathematics of curves.
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So, even a straight line, defined with calculus, is a curve.
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It's just a curve without inflection.
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So, a new vocabulary of form
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is now pervading all design fields:
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whether it's automobiles, architecture, products, etc.,
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it's really being affected by this digital medium of curvature.
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The intricacies of scale that come out of that --
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you know, in the example of the nose to the face,
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there's a fractional part-to-whole idea.
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With calculus, the whole idea
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of subdivision is more complex,
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because the whole and the parts are one continuous series.
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It's too early in the morning for a lecture on calculus,
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so I brought some images to just describe how that works.
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This is a Korean church that we did in Queens.
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And in this example, you can see
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that the components of this stair are repetitive,
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but they're repetitive without being modular.
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Each one of the elements in this structure
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is a unique distance and dimension,
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and all of the connections are unique angles.
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Now, the only way we could design that,
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or possibly construct it,
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is by using a calculus-based definition
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of the form.
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It also is much more dynamic,
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so that you can see that the same form opens and closes
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in a very dynamic way as you move across it,
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because it has this quality of vector in motion
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built into it.
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So the same space that appears to be a kind of closed volume,
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when seen from the other side becomes a kind of open vista.
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And you also get a sense of
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visual movement in the space,
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because every one of the elements is changing in a pattern,
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so that pattern leads your eye towards the altar.
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I think that's one of the main changes,
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also, in architecture:
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that we're starting to look now not for some ideal form,
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like a Latin cross for a church,
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but actually all the traits of a church:
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so, light that comes from behind from an invisible source,
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directionality that focuses you towards an altar.
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It turns out it's not rocket science
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to design a sacred space.
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You just need to incorporate a certain number of traits
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in a very kind of genetic way.
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So, these are the different perspectives of that interior,
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which has a very complex
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set of orientations all in a simple form.
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In terms of construction and manufacturing,
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this is a kilometer-long housing block
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that was built in the '70s in Amsterdam.
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And here we've broken the 500 apartments
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up into small neighborhoods,
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and differentiated those neighborhoods.
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I won't go into too much description of any of these projects,
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but what you can see is that
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the escalators and elevators
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that circulate people along the face of the building
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are all held up by
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122 structural trusses.
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Because we're using escalators
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to move people,
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all of these trusses are picking up diagonal loads.
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So, every one of them is a little bit different-shaped
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as you move down the length of the building.
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So, working with
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Bentley and MicroStation,
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we've written a custom piece of software
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that networks all of the components together
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into these chunks of information,
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so that if we change any element
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along the length of the building,
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not only does that change distribute
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through each one of the trusses,
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but each one of the trusses then distributes that information
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down the length of the entire facade of the building.
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So it's a single calculation
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for every single component of the building
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that we're adding onto.
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So, it's tens of millions of calculations
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just to design one connection between a piece of structural steel
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and another piece of structural steel.
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But what it gives us is a harmonic
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and synthesized
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relationship of all these components, one to another.
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This idea has, kind of, brought me into doing
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some product design,
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and it's because design firms
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that have connections to architects,
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like, I'm working with Vitra, which is a furniture company,
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and Alessi, which is a houseware company.
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They saw this actually solving a problem:
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this ability to differentiate components
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but keep them synthetic.
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So, not to pick on BMW,
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or to celebrate them,
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but take BMW as an example.
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They have to, in 2005,
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have a distinct identity
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for all their models of cars.
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So, the 300 series, or whatever their newest car is,
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the 100 series that's coming out,
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has to look like the 700 series,
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at the other end of their product line,
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so they need a distinct, coherent identity,
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which is BMW.
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At the same time, there's a person paying 30,000 dollars
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for a 300-series car,
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and a person paying 70,000 dollars
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for a 700 series,
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and that person paying more than double
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doesn't want their car to look too much like
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the bottom-of-the-market car.
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So they have to also discriminate between these products.
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So, as manufacturing
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starts to allow more
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design options,
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this problem gets exacerbated,
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of the whole and the parts.
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Now, as an architect, part-to-whole relationships
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is all I think about,
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but in terms of product design
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it's becoming more and more of an issue for companies.
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So, the first kind of test product we did
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was with Alessi,
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which was for a coffee and tea set.
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It's an incredibly expensive coffee and tea set;
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we knew that at the beginning. So, I actually went to some people I knew
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down south in San Diego,
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and we used an exploded
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titanium forming method
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that's used in the aerospace industry.
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Basically what we can do,
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is just cut a graphite mold,
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put it in an oven, heat it to 1,000 degrees,
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gently inflate titanium that's soft,
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and then explode it at the last minute into this form.
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But what's great about it is,
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the forms are only a few hundred dollars.
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The titanium's several thousand dollars, but the forms are very cheap.
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So, we designed a system here
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of eight curves that could be swapped,
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very similar to that housing project I showed you,
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and we could recombine those together,
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so that we always had ergonomic shapes
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that always had the same volume
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and could always be produced in the same way.
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That way, each one of these tools we could pay for with
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a few hundred dollars,
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and get incredible variation in the components.
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And this is one of those examples of the sets.
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So, for me, what was important is that
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this coffee set --
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which is just a coffee pot, a teapot,
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and those are the pots sitting on a tray --
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that they would have a coherence --
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so, they would be Greg Lynn Alessi coffee pots --
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but that everyone who bought one
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would have a one-of-a-kind object that was unique in some way.
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To go back to architecture,
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what's organic about architecture as a field,
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unlike product design,
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is this whole issue of holism
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and of monumentality is really our realm.
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Like, we have to design things which are coherent as a single object,
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but also break down into small rooms
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and have an identity of both the big scale
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and the small scale.
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Architects tend to work with signature,
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so that an architect needs a signature
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and that signature has to work across the scale of houses
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up to, say, skyscrapers,
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and that problem of signatures is a thing we're very good at maintaining
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and working with; and intricacy,
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which is the relationship of, say,
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the shape of a building, its structure, its windows,
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its color, its pattern. These are real architectural problems.
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So, my kind of hero for this in the natural world
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are these tropical frogs.
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I got interested in them because they're the most
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extreme example
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of a surface where
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the texture and the -- let's call it the decoration --
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I know the frog doesn't think of it as decoration, but that's how it works --
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are all intricately connected to one another.
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So a change in the form
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indicates a change in the color pattern.
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So, the pattern and the form aren't the same thing,
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but they really work together and are fused
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in some way.
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So, when doing a center
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for the national parks in Costa Rica,
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we tried to use that idea of a gradient color
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and a change in texture
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as the structure moves across the surface of the building.
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We also used a continuity of change
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from a main exhibition hall to a natural history museum,
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so it's all one continuous change
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in the massing,
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but within that massing are very different kinds of spaces and forms.
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In a housing project in Valencia, Spain, we're doing,
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the different towers of housing fused together
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in shared curves so you get a single mass,
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like a kind of monolith,
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but it breaks down into individual elements.
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And you can see that that change in massing
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also gives all 48 of the apartments
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a unique shape and size,
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but always within a, kind of, controlled limit,
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an envelope of change.
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I work with a group of other architects.
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We have a company called United Architects.
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We were one of the finalists for the World Trade Center site design.
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And I think this just shows how
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we were approaching
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the problem of incredibly large-scale construction.
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We wanted to make a kind of Gothic cathedral
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around the footprints of the World Trade Center site.
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And to do that, we tried to connect up
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the five towers into a single system.
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And we looked at, from the 1950s on,
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there were numerous examples of other architects
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trying to do the same thing.
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We really approached it at the level
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of the typology of the building,
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where we could build these five separate towers,
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but they would all join at the 60th floor
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and make a kind of single monolithic mass.
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With United Architects, also,
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we made a proposal for the European Central Bank headquarters
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that used the same system,
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but this time in a much more monolithic mass,
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like a sphere.
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But again, you can see this, kind of,
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organic fusion
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of multiple building elements
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to make a thing which is whole, but breaks down into smaller parts,
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but in an incredibly organic way.
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Finally, I'd like to just show you
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some of the effects of using digital fabrication.
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About six years ago, I bought one of these CNC mills,
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to just replace, kind of,
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young people cutting their fingers off all the time building models.
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And I also bought a laser cutter
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and started to fabricate within my own shop,
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kind of, large-scale building elements and models,
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where we could go directly to the tooling.
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What I found out is that the tooling,
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if you intervened in the software,
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actually produced decorative effects.
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So, for these interiors, like this shop in Stockholm, Sweden,
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or this installation wall in the Netherlands
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at the Netherlands Architecture Institute,
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we could use the texture that the tool would leave
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to produce a lot of the spatial effects,
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and we could integrate the texture of the wall
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with the form of the wall with the material.
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So, in vacuum-formed plastic, in fiberglass,
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and then even at the level of structural steel,
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which you think of as being linear and modular.
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The steel industry is so far
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ahead of the design industry
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that if you take advantage of it
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you can even start to think of beams and columns
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all rolled together into a single system
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which is highly efficient,
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but also produces decorative effects
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and formal effects
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that are very beautiful and organic.
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Thanks very much.
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About this website

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