How to pronounce "subdivision"

What I thought I would talk about today

is the transition from one mode

of thinking about nature

to another that's tracked by architecture.

What's interesting about architects is,

we always have tried to justify beauty

by looking to nature,

and arguably, beautiful architecture

has always been looking at a model of nature.

So, for roughly 300 years,

the hot debate in architecture

was whether the number five

or the number seven

was a better proportion to think about architecture,

because the nose was one-fifth of your head,

or because your head was one-seventh of your body.

And the reason that that was the model

of beauty and of nature

was because the decimal point had not been invented yet --

it wasn't the 16th century --

and everybody had to dimension a building

in terms of fractions,

so a room would be dimensioned

as one-fourth of a facade;

the structural dais of that might be dimensioned as 10 units,

and you would get down to the small elements

by fractional subdivision:

finer and finer and finer.

In the 15th century, the decimal point was invented;

architects stopped using fractions,

and they had a new model of nature.

So, what's going on today

is that there's a model of natural form

which is calculus-based

and which is using digital tools,

and that has a lot of implications

to the way we think about beauty and form,

and it has a lot of implications in the way we think about nature.

The best example of this would probably be the Gothic,

and the Gothic was invented after the invention of calculus,

although the Gothic architects

weren't really using calculus to define their forms.

But what was important is,

the Gothic moment in architecture was the first time

that force and motion was thought of in terms of form.

So, examples like Christopher Wren's King's Cross:

you can see that the structural forces of the vaulting

get articulated as lines, so you're really actually seeing

the expression of structural force and form.

Much later, Robert Maillart's bridges,

which optimize structural form

with a calculus curvature almost like a parabola.

The Hanging Chain models of Antonio Gaudi,

the Catalan architect.

The end of the 19th century, beginning of the 20th century,

and how that Hanging Chain model

translates into archways

and vaulting.

So, in all of these examples,

structure is the determining force.

Frei Otto was starting to use foam bubble diagrams

and foam bubble models to generate his Mannheim Concert Hall.

Interestingly, in the last 10 years

Norman Foster used a similar heat thermal transfer model

to generate the roof of the National Gallery,

with the structural engineer Chris Williams.

In all these examples,

there's one ideal form,

because these are thought in terms of structure.

And as an architect, I've always found these kinds of systems

very limiting, because I'm not interested in ideal forms

and I'm not interested in optimizing to some perfect moment.

So, what I thought I would bring up is

another component that needs to be thought of,

whenever you think about nature,

and that's basically the invention of

generic form in genetic evolution.

My hero is actually not Darwin;

it's a guy named William Bateson,

father of Greg Bateson, who was here for a long time in Monterey.

And he was what you'd call a teratologist:

he looked at all of the monstrosities and mutations

to find rules and laws, rather than looking at the norms.

So, instead of trying to find the ideal type

or the ideal average,

he'd always look for the exception. So, in this example,

which is an example of what's called Bateson's Rule,

he has two kinds of mutations of a human thumb.

When I first saw this image, 10 years ago,

I actually found it very strange and beautiful at the same time.

Beautiful, because it has symmetry.

So, what he found is that in all cases of thumb mutations,

instead of having a thumb,

you would either get another opposable thumb,

or you would get four fingers.

So, the mutations reverted to symmetry.

And Bateson invented

the concept of symmetry breaking,

which is that

wherever you lose information in a system,

you revert back to symmetry.

So, symmetry wasn't the sign of order and organization --

which is what I was always understanding, and as is an architect --

symmetry was the absence of information.

So, whenever you lost information, you'd move to symmetry;

whenever you added information to a system, you would break symmetry.

So, this whole idea of natural form shifted at that moment

from looking for ideal shapes

to looking for a combination of

information and generic form.

You know, literally after seeing that image,

and finding out what Bateson was working with,

we started to use these rules for symmetry breaking and branching

to start to think about architectural form.

To just talk for a minute about the

digital mediums that we're using now

and how they integrate calculus:

the fact that they're calculus-based

means that we don't have to think about dimension

in terms of ideal units

or discreet elements.

So, in architecture we deal with

big assemblies of components,

so there might be up to, say,

50,000 pieces of material

in this room you're sitting in right now

that all need to get organized.

Now, typically you'd think that they would all be the same:

like, the chairs you're sitting in would all be the same dimension.

You know, I haven't verified this, but it's the norm

that every chair would be a slightly different dimension,

because you'd want to space them all out for everybody's sight lines.

The elements that make up the ceiling grid and the lighting,

they're all losing their modular quality,

and moving more and more to these infinitesimal dimensions.

That's because we're all using calculus tools

for manufacturing and for design.

Calculus is also a mathematics of curves.

So, even a straight line, defined with calculus, is a curve.

It's just a curve without inflection.

So, a new vocabulary of form

is now pervading all design fields:

whether it's automobiles, architecture, products, etc.,

it's really being affected by this digital medium of curvature.

The intricacies of scale that come out of that --

you know, in the example of the nose to the face,

there's a fractional part-to-whole idea.

With calculus, the whole idea

of subdivision is more complex,

because the whole and the parts are one continuous series.

It's too early in the morning for a lecture on calculus,

so I brought some images to just describe how that works.

This is a Korean church that we did in Queens.

And in this example, you can see

that the components of this stair are repetitive,

but they're repetitive without being modular.

Each one of the elements in this structure

is a unique distance and dimension,

and all of the connections are unique angles.

Now, the only way we could design that,

or possibly construct it,

is by using a calculus-based definition

of the form.

It also is much more dynamic,

so that you can see that the same form opens and closes

in a very dynamic way as you move across it,

because it has this quality of vector in motion

built into it.

So the same space that appears to be a kind of closed volume,

when seen from the other side becomes a kind of open vista.

And you also get a sense of

visual movement in the space,

because every one of the elements is changing in a pattern,

so that pattern leads your eye towards the altar.

I think that's one of the main changes,

also, in architecture:

that we're starting to look now not for some ideal form,

like a Latin cross for a church,

but actually all the traits of a church:

so, light that comes from behind from an invisible source,

directionality that focuses you towards an altar.

It turns out it's not rocket science

to design a sacred space.

You just need to incorporate a certain number of traits

in a very kind of genetic way.

So, these are the different perspectives of that interior,

which has a very complex

set of orientations all in a simple form.

In terms of construction and manufacturing,

this is a kilometer-long housing block

that was built in the '70s in Amsterdam.

And here we've broken the 500 apartments

up into small neighborhoods,

and differentiated those neighborhoods.

I won't go into too much description of any of these projects,

but what you can see is that

the escalators and elevators

that circulate people along the face of the building

are all held up by

122 structural trusses.

Because we're using escalators

to move people,

all of these trusses are picking up diagonal loads.

So, every one of them is a little bit different-shaped

as you move down the length of the building.

So, working with

Bentley and MicroStation,

we've written a custom piece of software

that networks all of the components together

into these chunks of information,

so that if we change any element

along the length of the building,

not only does that change distribute

through each one of the trusses,

but each one of the trusses then distributes that information

down the length of the entire facade of the building.

So it's a single calculation

for every single component of the building

that we're adding onto.

So, it's tens of millions of calculations

just to design one connection between a piece of structural steel

and another piece of structural steel.

But what it gives us is a harmonic

and synthesized

relationship of all these components, one to another.

This idea has, kind of, brought me into doing

some product design,

and it's because design firms

that have connections to architects,

like, I'm working with Vitra, which is a furniture company,

and Alessi, which is a houseware company.

They saw this actually solving a problem:

this ability to differentiate components

but keep them synthetic.

So, not to pick on BMW,

or to celebrate them,

but take BMW as an example.

They have to, in 2005,

have a distinct identity

for all their models of cars.

So, the 300 series, or whatever their newest car is,

the 100 series that's coming out,

has to look like the 700 series,

at the other end of their product line,

so they need a distinct, coherent identity,

which is BMW.

At the same time, there's a person paying 30,000 dollars

for a 300-series car,

and a person paying 70,000 dollars

for a 700 series,

and that person paying more than double

doesn't want their car to look too much like

the bottom-of-the-market car.

So they have to also discriminate between these products.

So, as manufacturing

starts to allow more

design options,

this problem gets exacerbated,

of the whole and the parts.

Now, as an architect, part-to-whole relationships

is all I think about,

but in terms of product design

it's becoming more and more of an issue for companies.

So, the first kind of test product we did

was with Alessi,

which was for a coffee and tea set.

It's an incredibly expensive coffee and tea set;

we knew that at the beginning. So, I actually went to some people I knew

down south in San Diego,

and we used an exploded

titanium forming method

that's used in the aerospace industry.

Basically what we can do,

is just cut a graphite mold,

put it in an oven, heat it to 1,000 degrees,

gently inflate titanium that's soft,

and then explode it at the last minute into this form.

But what's great about it is,

the forms are only a few hundred dollars.

The titanium's several thousand dollars, but the forms are very cheap.

So, we designed a system here

of eight curves that could be swapped,

very similar to that housing project I showed you,

and we could recombine those together,

so that we always had ergonomic shapes

that always had the same volume

and could always be produced in the same way.

That way, each one of these tools we could pay for with

a few hundred dollars,

and get incredible variation in the components.

And this is one of those examples of the sets.

So, for me, what was important is that

this coffee set --

which is just a coffee pot, a teapot,

and those are the pots sitting on a tray --

that they would have a coherence --

so, they would be Greg Lynn Alessi coffee pots --

but that everyone who bought one

would have a one-of-a-kind object that was unique in some way.

To go back to architecture,

what's organic about architecture as a field,

unlike product design,

is this whole issue of holism

and of monumentality is really our realm.

Like, we have to design things which are coherent as a single object,

but also break down into small rooms

and have an identity of both the big scale

and the small scale.

Architects tend to work with signature,

so that an architect needs a signature

and that signature has to work across the scale of houses

up to, say, skyscrapers,

and that problem of signatures is a thing we're very good at maintaining

and working with; and intricacy,

which is the relationship of, say,

the shape of a building, its structure, its windows,

its color, its pattern. These are real architectural problems.

So, my kind of hero for this in the natural world

are these tropical frogs.

I got interested in them because they're the most

extreme example

of a surface where

the texture and the -- let's call it the decoration --

I know the frog doesn't think of it as decoration, but that's how it works --

are all intricately connected to one another.

So a change in the form

indicates a change in the color pattern.

So, the pattern and the form aren't the same thing,

but they really work together and are fused

in some way.

So, when doing a center

for the national parks in Costa Rica,

we tried to use that idea of a gradient color

and a change in texture

as the structure moves across the surface of the building.

We also used a continuity of change

from a main exhibition hall to a natural history museum,

so it's all one continuous change

in the massing,

but within that massing are very different kinds of spaces and forms.

In a housing project in Valencia, Spain, we're doing,

the different towers of housing fused together

in shared curves so you get a single mass,

like a kind of monolith,

but it breaks down into individual elements.

And you can see that that change in massing

also gives all 48 of the apartments

a unique shape and size,

but always within a, kind of, controlled limit,

an envelope of change.

I work with a group of other architects.

We have a company called United Architects.

We were one of the finalists for the World Trade Center site design.

And I think this just shows how

we were approaching

the problem of incredibly large-scale construction.

We wanted to make a kind of Gothic cathedral

around the footprints of the World Trade Center site.

And to do that, we tried to connect up

the five towers into a single system.

And we looked at, from the 1950s on,

there were numerous examples of other architects

trying to do the same thing.

We really approached it at the level

of the typology of the building,

where we could build these five separate towers,

but they would all join at the 60th floor

and make a kind of single monolithic mass.

With United Architects, also,

we made a proposal for the European Central Bank headquarters

that used the same system,

but this time in a much more monolithic mass,

like a sphere.

But again, you can see this, kind of,

organic fusion

of multiple building elements

to make a thing which is whole, but breaks down into smaller parts,

but in an incredibly organic way.

Finally, I'd like to just show you

some of the effects of using digital fabrication.

About six years ago, I bought one of these CNC mills,

to just replace, kind of,

young people cutting their fingers off all the time building models.

And I also bought a laser cutter

and started to fabricate within my own shop,

kind of, large-scale building elements and models,

where we could go directly to the tooling.

What I found out is that the tooling,

if you intervened in the software,

actually produced decorative effects.

So, for these interiors, like this shop in Stockholm, Sweden,

or this installation wall in the Netherlands

at the Netherlands Architecture Institute,

we could use the texture that the tool would leave

to produce a lot of the spatial effects,

and we could integrate the texture of the wall

with the form of the wall with the material.

So, in vacuum-formed plastic, in fiberglass,

and then even at the level of structural steel,

which you think of as being linear and modular.

The steel industry is so far

ahead of the design industry

that if you take advantage of it

you can even start to think of beams and columns

all rolled together into a single system

which is highly efficient,

but also produces decorative effects

and formal effects

that are very beautiful and organic.

Thanks very much.