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Paola Antonelli + Benoit Mandelbrot
The curator and the mathematician discuss fractals, architecture, and
the death of Euclid.
by Edit Staff • Posted March 24, 2008 11:54 PM
Paola Antonelli is senior curator of Architecture and Design at The
Museum of Modern Art. Benoit Mandelbrot is the father of fractal
geometry. While studying architecture at the Politecnico in Milan in the
1970s, Antonelli was inspired by Mandelbrot's geometric ideas and
visualizations, and eventually wrote her thesis on "Fractal
Architecture." The two met for the first time last year when Antonelli
invited Mandelbrot to a Seed/MoMA Salon, a monthly gathering of
scientists, designers, and architects. Just before Antonelli's new
Design and the Elastic Mind exhibit opened at MoMA in February, they
reconnected to discuss fractals, architecture, and the death of Euclid.
Click on the image to watch highlights from the Salon.
Paola Antonelli: So, here we are. It's 18 years after my thesis, and I
finally get to meet you.
Benoit Mandelbrot: Well, everything happens if you live long enough!
PA: That's right! I'll tell you briefly what it was about, because I
just want to have your reaction. I was very, how should I put it...very
naive about the mathematics involved in your thinking.
BM: I am naive about the art.
PA: Well, I hope so. It was not art, it was architecture. In any case, I
had tried to read your first book about fractal geometry. Of course, I
was skimming through it, not understanding any of the equations, but I
noticed something: Some of the most recent architecture—and in
particular I was studying the work of Coop Himmelb(l)au, an
architectural group from Austria—could not be represented anymore
through plans, sections, and elevation. There was no way. Not even with
axonometry. Or perspective. Normal geometry just did not work.
Also, you couldn't photograph it; pictures wouldn't render the spaces at
all. The only way was to experience them. And somehow, without really
having any mathematical or any theoretical proof, I thought there was a
connection between your book and this kind of architecture.
So I decided to explore this theory and do my thesis on it, which was
called "Fractal Architecture." Now, thank God, it's only in Italian, so,
you will never... Oh, my God, maybe, you speak Italian!
BM: No, but I can read Italian.
PA: Oh, no, no. But, it's really just very interesting to see how your
theories, your geometry, and your work have had tremendous impact on the
world, even on people who didn't know about them. When I interviewed
Wolf Prix, who is the principal of Coop Himmelb(l)au, I asked him, "Do
you know anything about fractal geometry?" He said no.
I just found it really interesting. There's a real impact that your
science has on the world, and vice versa.
BM: Well, I've had a life, how to say it, full of adventures, though not
always by choice. Things were very complicated during World War II.
Altogether it never quite left me the leisure to decide who I was.
PA: Where were you?
BM: I was in central France, in an area you could describe as French
Appalachia. There were deep valleys, and people considered Parisians
foreigners. It's a very interesting place. It was not occupied, but was
very closely supervised by the Germans. And one didn't think of the
future particularly; the future was so distant. First survive and then
there'll be a future. So, I never really decided in which field I was
going to spend my life—a situation with pluses and many minuses. It's
one of the most peculiar and striking aspects of my scientific life.
But over the years I've recognized things that are very close to my work
and could not have conceivably been associated with mathematics.
PA: The power of fractals is that they're so instinctive. They're
immediately graspable even without knowing there's a geometric law
behind them.
BM: Well, that's the astoni****ng thing—and to me it was an amazing
surprise. I was very visual, of course, but I did not view myself as a
future scientist.
Mathematics in high school was easy but much less exciting than French
history or language. I did well, but it was not something very im****tant
to me. Then, I stopped school for a while, which turned out to be very
im****tant. I went on studying, but my way.
Once back at school, for each problem the professor posed, I had an
instant solution—never the same as his. My solutions involved shapes. So
I was taking these very dry questions that he asked, and without being
particularly conscious of my thinking process, solving them all—near
instantly—in terms of real shapes. This took no effort whatsoever. I
had, how to describe it? A very freakish gift. In every mathematical
question that was asked, I just saw something real that had the same
properties.
PA: The things that you saw, were they coming from the real world? Were
they coming from intuitions? What would you connect them to?
BM: They were coming from everywhere. During the period I wasn't in
school, and couldn't study systematically, I read a lot, whenever I
could. So I would remember many things through, how to say, mathematical
simplifications.
PA: So, you had the intuition and then you would recognize this
intuition in the things that you saw.
BM: Absolutely.
PA: I'm sure you know that your work has had tremendous impact in
architecture and in design, not only formally, but also philosophically.
The idea of the algorithm, of the growth of structures, and the growth
of objects. Who was the first architect or designer that contacted you
and wanted to talk about it and wanted to learn directly from you?
BM: Well, actually, I think that it wasn't that they came toward me. I
came toward them.
PA: Really? Interesting. So, who did you refer to?
Benoit Mandelbrot Credit: Julian Dufort
BM: Well, a paper I wrote, and that was widely quoted, concerned
fractals and architecture. It was in a certain sense a critique of the
Bauhaus. A very short paper, but very influential.
I focused on Mies van der Rohe and the Seagram Building because of my
anger against Mies van der Rohe's misunderstanding of something I very
much care about. By contrast, take Charles Garnier, who primarily
designed the opera houses in Paris and Monte Carlo.
He was not very popular, but represented—at least for somebody with a
French education—the kind of principle of what architecture should do.
PA: Meaning?
BM: Meaning, for example, walking toward the Garnier opera house in
Paris, from far away, the most striking thing is the roof. You come
closer, other things appear, but they are always of approximately the
same degree of complication.
Whereas Mies van der Rohe seen from a distance is just a big box. As you
get closer you see a grid of windows on the box, and as you get really
close, you can see some some things of whoever lives behind the windows.
The building itself had the smallest number of scales imaginable. It is
very simple to describe. And the architect was proud of it.
PA: Of course he was! He simply was not going after the same effect
you're talking about, which is organicism in architecture. That's truly
what you are praising. But, somehow you also need to have complete
abstraction and the simplification of details in order to be able to
appreciate organicism. Modern architecture had a reason to exist.
BM: Well, modern architecture had two reasons to exist. One is the
desire, on the part of architects, to be different. And the other is the
desire, on the part of the builders, to be cheap. Look at modern
architecture in early manifestations, for example, in Russian building
designs shortly after the revolution—many of which were never actually
built, for lack of funding. They were very conscious of the fact that
this was not something beautiful.
So, Garnier, who, again, was not a creative genius, but was a
representative of a certain school of architecture, put it very, very
strongly. From a distance, you could see something, and as you come
closer, you see something else but always of the same kind.
PA: That's like medieval architecture. It's like the Cathedral of Milan.
Yeah, I understand.
BM: Absolutely, and this is so much more interesting architecturally and
aesthetically.
PA: What is really amazing to me right now is how contem****ary
architects are using the idea that is behind fractals, the idea of a
rule that lets them work at different scales indifferently, at least
until the moment when the real design application, the reality of the
client or manufacturer wanting a building or a toaster, sets in.
I am thinking, for instance, of Ben Aranda and Chris Lasch, who you may
remember spoke right after you when we had the salon at MoMA. They are
two architects that have founded their practice on understanding
algorithms and finding ways to take scientific concepts and translate
them for architecture's benefit and evolution.
So, it seems to me that it is not only and simply about the formal
beauty of fractals, it is the idea of growth that your theory has really
given to architects and designers.
And now we're seeing the algorithm become the principle, and the subject
of research, for so many architects today. They're hoping that they can
ultimately input an algorithm, give it a push, and then all of a sudden
an object, a building, a city, and a world will grow out of it.
BM: Well, that would be very exciting and I am very pleased to hear you
say it. I have, of course, a good inkling of it. I can speak of other
great masters, or unknown masters, who proposed no principle, recorded
neither reasons nor comments, but did work along these lines. So, the
long time it took for this to be codified is astoni****ng. It's
astoni****ng that the motivation behind these other great works was not
more actively pursued. Because they are manifestations of the fact that
certain numeric ideas are permanent.
I am not only a scientist, and I find it very im****tant that great
architects have very often followed the same path as scientists. And
now, it seems, the evolution of these ideas continues in the kind of
architecture you describe, this time with a scientific spine.
But in the past, nobody could understand them, nobody could appreciate
what was behind them and so they weren't often recorded. But, well,
history has its own funny ways.
PA: In a way it is almost a fractal attitude, an indifference to time;
the past and the present and the future have the same instinctive
approach to things.
BM: Ha, yes. It's mind-boggling.
FROM CUBES TO FRACTALS
PA: I would like to ask you about some major phenomena that have
happened in the world since the publication of your books, phenomena
that seem almost manifestations of fractals in the world. One is the
internet, for instance.
BM: I was well placed to know about the internet since of course it
became very im****tant when I worked for many years at IBM. And
colleagues mentioned to me some strange things about the way in which
the internet became organized. There was no single overall architect and
many things were happening by local decisions. A terrible mess ensued
and the question was, can you see any order in that mess? I was pleased
to discover some order, though it was not my field.
PA: And what about contem****ary architecture? Have you seen the idea of
fractals translated in a particularly powerful way in recent architecture?
BM: My influence may or may not have helped, but certainly the mood is
different. Most of modern architecture was, how to say, cheap. For
example, driving from de Gaulle air****t into Paris, you go by many
buildings that are absolutely abominable.
They are cubes of the worst kind and I would hate to live there.
Admiration for this simplified art, this Euclidean architecture, which
sticks to cylinders or cubes or parallelepipeds, was very short-lived.
And most people didn't like it. The profession, I'm sure, had no choice
at the time. A few people enjoyed it, a few people got a good name for
it. But at this point, I think it's safe to say the idea that perfection
is a cube is over.
PA: Hmm.
BM: I remember, afterwards, when suddenly fractals became all the rage,
at least in some schools. And I was afraid it would just die off like
many little fads. But in fact, it continues.
This has been for me an extraordinary pleasure because it means a
certain misuse of Euclid is dead. Now, of course, I think that Euclid is
marvelous, he produced one of the masterpieces of the human mind. But it
was not meant to be used as a textbook by millions of students century
after century. It was meant for a very small community of mathematicians
who were describing their works to one another. It's a very complicated,
very interesting book which I admire greatly. But to force beginners
into a mathematics in this particular style was a decision taken by
teachers and forced upon society. I don't feel that Euclid is the way to
start learning mathematics. Learning mathematics should begin by
learning the geometry of mountains, of humans. In a certain sense, the
geometry of...well, of Mother Nature, and also of buildings, of great
architecture.
Now, do you think I'm just having dreams of grandeur in my old age, or
is it true that I provided mathematics with a wider audience? I get
letters all the time from high school students, from all kinds of
places, and they often begin by saying: "Well, we just realized that you
are still alive! We thought you'd be long dead." Which is a bit...well,
I mean...
PA: Flattering!
BM: I'm getting used to it. But what do you think; don't you think that
mathematics like this is more alive, warmer? That it is catching?
Paola Antonelli Credit: Julian Dufort
PA: What really helped fractal geometry and its application in school, I
think, is the computer. Having computers in classrooms has been a
blessing for all sorts of more visual and more organically based forms
of geometry and mathematics.
It helped popularize the idea of fractal geometry and make it become
more comfortable and easier for people to accept. And then it also
became something for the more elite culture of architects and designers
to adopt. I wonder whether the idea of the use of algorithms in
architecture was introduced not only by biology, but also a lot by
fractals.
And the fact that there is more and more science in many architects' and
designers' work is very telling. Before, science was kept at bay, and
architecture found its inspiration elsewhere; now, science instead
appears to be more immediately useful and present in their vocabulary,
perhaps because it has gotten so much closer to a real description of
the world.
BM: At one point in history a copy of Euclid was ****pped from Spain to
Italy, and translated. It provoked an extraordinary change in very many
aspects of life.
To begin with, it was read by architects and painters; Giotto, a great
painter, had no idea of perspective, so he was incapable of representing
the beams in that amazing long refectory that he painted.
However, after Euclid became known, his geometry could be taught to
anybody. Therefore, there was a moment in history when a mathematics,
very different from anything that existed before, came back to the West
by the intermediary of Italian painters. This may or may not have
contributed to the greatness of the Italian Renaissance.
So, mathematics can have a direct influence on everybody's world.
Earlier mathematics had developed very separately from the world. Early
on, Euclid was very far from everyday reality; but then the world
changed, and mathematics became indispensable.
THE NEW GENERALISTS
BM: So I know that you are preparing an upcoming exhibit at the museum.
I've visited it many times, and each time, it's bigger!
PA: It is definitely bigger.
BM: And each time it's more varied. But tell me, what viewpoint or
theory or approach do you hope to foster with this exhibit?
PA: My specialty, my passion, is contem****ary design. I'm trained in
architecture, and I am proud to spontaneously spot traces of the
indifference to scale that you preach, I view architecture, urban
planning, design, objects as theoretically the same.
This particular exhibition, which is called "Design and the Elastic
Mind," comes 14 years after I started at MoMA. With every exhibition,
I've tried to show people the im****tance of design, and this time I
found a very strong alignment with science.
Interestingly, both design and science are trying to change their
position in people's perception. Science is trying to be perceived as
more part of the real world and less lofty than before, and designers
are tired of being considered decorators, because they have a much more
structural roles in shaping people's lives. They really anticipate
behaviors and guide change.
Designers take scientific revolutions and they make them usable and
exploitable, comprehensible to the average human being. The internet is
an example: it used to be lines of code, and then the designers came. It
became an interface, and now we're using it.
So this particular show is about how designers and scientists work
together—how they worked together two years ago and how they'll work
together in two years. It's about the present. It's about the
discoveries that are being made right now.
BM: Ah, interesting.
PA: There's a very strong component of nanophysics and nanotechnology
and how they can help shape a model of collaboration for science and
design in the future.
Something that is truly interesting, that Peter Galison at Harvard first
talked about, is the idea of "nanofacture"—the idea that scientists are
compelled to become designers because of the possibility of building
things atom by atom. And you might have given them a hint already, with
fractals, because it was already something playful that they could do.
Scientists are designing. And designers are trying to learn about
science and collaborating with scientists. And together, they are trying
to help people cope with the tremendous changes in everyday life—in
scale, in resolutions of screen, in contact with big crowds of people...
And what I hope, as I do with every show, is that people will recognize
themselves in it. I hope that people will immediately say, "Oh my, this
happens to me, too," and therefore understand the role of design—and
this time, also of science—in their everyday life.
BM: Well, it is very encouraging for me, because I'm an old man and, as
I always mention at some point, I never made up my mind who I really
was, which allowed me to spend my life on many things. So what you're
telling me is that I can just relax, because I won't have to decide!
PA: I don't know. You're very responsible for what goes on right now. I
don't think you can relax any time soon!
BM: Well, yes, but at least I won't have to become a specialist, because
everybody is going to become a generalist.
PA: Generalism is very im****tant. The interesting aspect of your theory
was that it was very easy to generalize. And I'm not saying it as a
disadvantage; I'm saying it as a quality. It's possible to grasp it,
even if you are not a scientist or really versed in mathematics.
So I think that your ideas and your approach were almost the beginning
of generalism. And designers are big generalists, and scientists are
trying to become a little more generalist because sometimes they feel
that they have become too specialized.
But I think you can't sit down and relax quite yet, because you see what
happens when architects like Ben and Chris get ahold of you. Discussions
go into the wee hours of the morning. I think that the immediate
application of your ideas, in design and architecture, has only just now
begun to happen.
BM: Great news.
PA: Yes, it is.
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Paola Antonelli + Benoit Mandelbrot, written by Edit Staff, posted on
March 24, 2008 11:54 PM, is in the category The Seed Salon. 9 blog
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