FacebookTwitterYoutubeInstagramGoogle Plus

Why are we drawn to symmetry? Because it provides order in a seemingly chaotic world? Because our brains are the product of the very same laws that yield the flower, the snowflake and the solar system? Because evolution selects for structures with symmetry? In this Salon, we will ask an interdisciplinary gathering of artists and scientists to explore the pervasiveness of symmetry throughout our study and appreciation of the natural world. This program is part of the Big Ideas Series, made possible with support from the John Templeton Foundation.Learn More

View Additional Video Information


ROBBERT DIJKGRAAF, MATHEMATICAL PHYSICIST: Good afternoon, great to have you here, this Salon one of the last performances here of the World Science Festival and this afternoon’s topic is beauty and balance- and we take this occasion to have a discussion about the role of symmetry. Symmetry in science and mathematics. I will be representing the sciences but also in the arts and I hope this will for all of us be a wonderful occasion to have a conversation that might be even more broader ranging about the connection between art and science about the way we are guided by mathematical principles or not what our concepts of beauty are of order of chaos of asymmetry. I think it’s just a grant topic that I hope to explore with my two panelists but also with you at some point I think I would really want to direct give you the opportunities to ask a few questions.

So I think we are all set up for a lovely afternoon and I think this is the right moment to call my two participants as I said you know we have the arch we presented here both by design and architecture. And the first participant I want to ask our first speaker is the senior curator at the Museum of Modern Art in the Department of Architecture and Design. He’s also MoMA’s founding director of research and development.  And her work investigates designs influence on everyday experience. Please say hello to Paola Antonelli.

Welcome Paola, please have a seat. And then our third participant is also joining us is the principal architect of Selldorf Architects the 65 person architectural design practice founded in New York City in 1988 and the firm creates public and private spaces that manifests a clear and modern sensibility to enduring impact. Please welcome architect Annabelle Selldorf.

A both warm welcome to you, Paola and Annabelle. I think we said to the audience, you know we’ll try to make this as interacting a conversation as possible and some part also involves the audience and we have kind of a grand topic today because it’s- Although we were asked to speak about the role of symmetry in science and art and we will do so in the beginning.

We want a sense- and we are in some sense free since this also is basically the last solo of the science festival to do anything that we like and we’re just going to go anywhere and I’m sure the audience will be cheering us on! But in order to fulfill all our contractual obligations or to say we start by speaking a little bit about symmetry. And I think you know my role is here to say a few words about how symmetry is viewed from the perspective of a mathematician or physicist which I am. And then I will ask each of you to say something briefly about I would say the canonical… just bring us up to speed is what typically is kind of what the typical thoughts are that go both in design and architecture thinking about symmetry.

So if I can start. Now, I think the symmetries clearly are all around us. No, if it wouldn’t be so dark in this room I would kind of ask the audience to point out symmetrical objects but clearly the room is left right symmetric to a large extent then. Now for us if you look in nature we see many manifestations of it from just a set the stage from a mathematical perspective asymmetry is usually seen as a movement so you can think of reflecting something turning left and right or rotating something around or shifting something along a certain distance.

And in general if you do that, the object changes. It’s different. But if it’s symmetric then it doesn’t. So for instance, a snowflake if we turn it around 60 degrees. It has a hexagonal symmetry- it actually comes back to itself. If you have a checkerboard you move it along one or two steps then actually it returns to its original state so it’s also about invariance. It also has to do with information in some sense because it’s a motion you apply to an object that doesn’t create something else. That’s kind of the traditional bowl of symmetries as it was understood by the Greeks. And but then it has this tremendous story in the development of science where more and more- and I hope we can have a discussion about- became a guiding principle. So I think if you would say to your modern scientists. And particularly if you’re interested in understanding the deep structures in reality what can you have as a guiding principle what symmetry is one of these. So it’s one of the most fundamental tools we have. And it’s in many ways I think also a manifestation of deep water is there in nature that we all love and that’s why scientists have a job because I can do something to discover there and understand. So this kind of mathematical perspective I just catch it here. Come back with perhaps in later stages but perhaps I can turn to you Paola if you… Just in broad brushes describe the role of symmetry in design. What what would you…?

[00:05:57] PAOLA ANTONELLI, MOMA CURATOR:Annabelle will talk about architecture but architects and designers forever and human beings in general in their making of things have been trying to imitate nature because nature does it best. And one of the rules that they have read in nature is this rule of symmetry which as we know very well is not completely real but nonetheless by trying to simplify in order to then imitate, they set out to first and foremost try symmetry so try from the first and if it doesn’t work we can move on. So when it comes to the Museum of Modern Art it was founded in 1929 and interestingly it was founded by three ladies of The New York Society that wanted to show how non-symmetrical modern art really was. In a way where they were trying to show something other than the old master’s collection of their husbands. So I don’t know if you had that picture of the Museum of Modern Art’s trustees looking at the Picasso paintings but already the museum was founded in 1929 and in 1930 already there were these major exhibitions of Picasso. And clearly if you think you see here the (French word???) in the early 1930s that was the idea of the art that they wanted to show.

DIJKGRAAF: But at the same time design instead was shown for its Platonic beauty and freedom in going to the images of those pieces of machinery coils and propellers. There was an exhibition in 1934 at MoMA that was considered revolutionary, it was a design show, it was called “Machine Art”. And there were all these propellers and ball bearings and coils at exactly this one that were shown on white pedestals as if they were bronchus’ (?) sculptures and against white backgrounds. It was really revolutionary. Nobody had shown design that way. And the two curators got a lot of flack for it but to us this exhibition that was so innovative at that time might seem old fashioned today because it was all about the Platonic beauty and the symmetry of these highly functional objects. And Phillip Johnson, the curator, used this term “Platonic beauty”, and–

DIJKGRAAF: It’s a good image by the way because of course Plato describes these objects.


DIJKGRAAF: And it’s as of course often the kind of it’s interesting you also said… well it’s difficult to find an entirely symmetric object in nature.


DIJKGRAAF: But of course Plato is in my mind, you know you can have the perfect hexagon, you can have the perfect spiral. So why come back to this point? Why these objects, why did they actually demonstrate symmetry, what is this issue telling us?

DIJKGRAAF: They were made… The designers were not trying to demonstrate symmetry they were trying to make objects as efficient as possible and therefore the symmetrical quality was also connected to the fact that most of them were parts of engines where… like working things.  And it’s interesting.

DIJKGRAAF: Let me come back to that point. The fact that symmetry is actually emerging in some sense in terms of efficiency.

ANTONELLI: As a goal, exactly. But then in the years that went between that exhibition and today so much has changed and especially the concept of beauty has changed which I know we’re going to talk about later. So it’s not only Picasso it’s also Almodovar, it’s David Bowie, it’s Muhammad Ali you know just to talk about the people that have brought us beyond the idea that something perfectly balanced is perfect. And today we have come to embrace them in an age in which so many things can be perfectly symmetrical we’ve come to really- in the world of design and in the world of architecture- to praise also a symmetry and lack of balance. I remember how… this is kind of jumping, but how excited I was when I saw that there is a company in Portugal called “fruita fea” which means “ugly fruit” that takes all the kind of like… knobby and kind of ugly fruits you know like the apples that are completely asymmetrical and that nobody wants and then sells them to you for a very low price but they were showing these beautiful baskets of really weird–

[00:10:20] DIJKGRAAF: Instead of the Platonic apple…

ANTONELLI: Yes! The non-Platonic is so much more interesting.

DIJKGRAAF: I must say we saw briefly the image of the apple there and I think anybody at home… if you know it then it’s a simple fact, but the fact that an apple has a five fold symmetry. Many people do not know so because usually you cut an apple in four because you cut it in five just because an apple so the middle and be amazed to see the five fold symmetry. I just want to get- perhaps I can almost summarize part of what you said is that- in design it’s this kind of a slow reading of this kind of idea of symmetry and perfection as a goal, and going to more… the asymmetric.

DIJKGRAAF: Yeah but it has to do also with the computational power that has made us even more able and more eager to get close to nature.


ANTONELLI: And by using compressional power we’ve discovered that symmetry is not the most important secret that we can use from nature in order to build.

DIJKGRAAF: We go beyond.


DIJKGRAAF: Annabelle, you would have a similar view on the role of symmetry in architecture?


DIJKGRAAF: Good! (laughs)

SELLDORF: Not at all because I think in the first place it’s not necessary to assign a value to either because I think that symmetry is simply a fact. It’s a state, it’s a concept. And how it was used in- or how it is used in architecture is… in a way if you will… a milestone. I think classical architecture obviously is is very much based on the idea of symmetry. We can see it right there. The Greeks only ever used even numbers for example in their colonnades so that you never had a column in the middle that therefore had to split to science. Anyway, and there are many different kinds of symmetry but architecture and design probably in the 20th century or later 20th century have given symmetry a bad rap as if like it’s boring to be symmetrical. But-

DIJKGRAAF: Well it is boring to be symmetrical in the technical sense that if you if something is perfectly symmetric if you’ve seen half of it you’ve seen all of it, right?

SELLDORF: I think it’s uninteresting to always assign values to everything. I think instead when you decide was deliberate effort to make something asymmetrical you still use symmetry as a reference, right? So in some ways for me as an architect today I think symmetry is a tool as much as asymmetry is a tool. There’s a wonderful image of Frank Lloyd Wright’s um… Falling Water that is all about these ideas of approaching nature and tolerance and so forth. So I do agree that symmetry isn’t the only thing that gives us consideration but it’s a point of departure in some ways.  And and I think it’s something that’s hard to get around. Our faces-

DIJKGRAAF: You must think that they kind of already transpired a little bit particularly because we went back to kind of the ancient times or something that would you say from that frame of mind, symmetry was kind of equal to perfection or the two things had something to do with it. Is it about approaching something of a perfect state?

SELLDORF: Well the concept of perfection is so incredibly difficult that- take the Japanese concept for example- where perfection only happens if a break with the complete surface actually happens. And… there is a saying that I can’t bring to mind right now. But in my mind more than anything the reason why symmetry is interesting is because it is a concept and because it exists whether we like it or not.  So to use that as a as a point of departure is I think what’s interesting.

DIJKGRAAF: I was also wondering you know if you go back to the act of making something. I already start to know if you were a physicist and you want to understand the world you look for guiding principles and some of the guiding principles are that if you have symmetry considerations it constrains very much the forms of the theory in which you describe the world. For instance know if you want described a world in a way that it doesn’t really depend how your precise orientation is. Sort of like it doesn’t really matter whether the forces in it are going North or East or West or South. So it’s an important guiding principle. In some sense can both you… perhaps start with you Paola… if you are a designer or something: What is symmetry also kind of a tool is it something you can use or is it the guiding principle for some designers or–

[00:15:41] SELLDORF: It is for some designers there are so many forms of design, it’s almost dizzying. So there’s the good old fashioned furniture design, there’s the product design in which you make things that go into the market, and then you also have visualization designing which you take data and you render them in a visual form that makes them better understandable.

SELLDORF: There is interface designer, there is video game design- so it really is as huge as can be. But let’s go to the old fashioned kind of product design. In most cases product design tends to have symmetry as a rule and it has to do with both efficiency or the idea that you take something with your hands and sometimes it has to do also with manufacturing constraints. Like I’m thinking when you have rotation molding by definition rotation molding with which so many bad plastic furniture and you know many plastic objects are made- that’s rotation molding so you have a rotational symmetry. Similarly with some with some thermal plastics you have molds that are injected, injection molds that also are symmetrical so I would say that when it comes to physical objects in many- most cases. Yeah, these are the objects from the machine art show. But if you think of more recent objects just think of the M&Ms or think of the Post-it notes or think of so many other objects. They tend to be symmetrical. When you start getting the kind of design that is more generated by algorithms that is more organic, it tends to be not a rule but something that happens if it has to happen or not.

DIJKGRAAF: Yes. Well this does relate perhaps also to… by way… yesterday we had a symposium on symmetry in science and an important role was played by the fact that in general nature is not symmetric. But if you go to a special situation often in all of of minimal energy or you can think of it of trying to pack things in the most regular way. We discussed the shape of a soap bubble that tries to minimize its surface tension. You typically get symmetrical objects. In fact it’s efficient. I mean I think that’s why we see it in flowers, in organisms. So you’re basically making a point that if our tools of design and production will change and they are changing now where they are to some sense we see less and we probably will see in the future less and less symmetrical objects, are you thinking?

SELLDORF: I don’t know I think it’s just there’s the other big issue is symmetry which is beauty and we’ll deal with that later. So symmetry as a merchandising or marketing tool. But I think that as we have more and more added to design and 3-D printing and the idea so many architects and designers are working on growing objects and buildings as opposed to making them so when you have a pavillion that’s made by silkworms then you know the symmetry will not be that important anymore. So-

DIJKGRAAF: So kind of the difference when you think about it like a crystal or something which is just the way in which molecules are atoms are ordered compared to a tree which grows organically and completely different kind of shape.

SELLDORF: Absolutely, and that’s what many architects and designers that are doing experimental work right now are taking as models.

DIJKGRAAF: And also that you actually, as an architect in a leading architectural firm, do you see this symmetry as a guiding principle in your work or is it evolving in the same direction that Paola’s saying the old technology is changing–

SELLDORF: I think it’s largely evolving in the same direction as Paola said but in addition to that I think that with the onset of modernism we’ve sort of taken it as an intellectual concept to defy symmetry and I think that today and we’re actually past that because if there are reasons that symmetry is useful, so to speak, if you can employ it as a tool within a set of particular circumstances then so be it, as you said.  So I think it’s not so interesting to say yea or nay but I think it is interesting and sounds to me like eventually we’ll go talk about the concept of beauty relative to symmetry. There it really gets interesting because there are all sorts of social influences too, no? As an architect I find it highly annoying when somebody comes to me and says, “I really like symmetry.”

Audience: (Laugh)


ANTONELLI: Thank you for informing me, I’ll alert the media.

[00:20:35] DIJKGRAAF: Was that the reason why you came to this performance?

DIJKGRAAF: So since we know already, we said three times we will discuss about it. I think we should talk about a beauty.

DIJKGRAAF: My favorite line is that you know you talk about symmetry with the mathematicians or physicists they will say “Oh it’s beautiful!” and there’s not a little hint of irony in using that word. Actually my thesis is that the word beauty is only used without any conditions in a very naive fashion in science. It’s… in our design it’s something you have to put quotation marks you have to discuss it. We are still in this very naïve… ancient time where we just think it’s the highest appeal to describe. So how come, um, so let’s first discuss this point to why the association between beauty and symmetry? Before we go to perhaps take a view what happened in the last hundred years or something but could you say something about why do we even associate the word “beauty” with symmetrical objects?

SELLDORF: Isn’t it biological? Isn’t it that we’re attracted to… as human beings we used to be attracted in history to symmetry for reasons maybe that had to do with like optimal procreation. I don’t know but-

DIJKGRAAF: But if we look at the flower, I’m operating as a flower–

SELLDORF: We’re bilaterally symmetrical ourselves, so to start with there is a degree of comfort and comfort and familiarity I think with the idea of symmetry.

DIJKGRAAF: Is it by the way a kind of a universal cultural phenomenon-

SELLDORF: Absolutely- across all cultures… and all epochs.


SELLDORF: I think that the word, though, is Greek.


SELLDORF: No, symmetry.

ANTONELLI: Oh symmetry, yes.

SELLDORF: We’re still on symmetry, sorry. Um, and it means it includes proportion and balance in dimensional understanding or in a dimensional sense. And I think that sort of goes back to… to answering your question, is that is, why we sort of, are we almost cannot do without the concept of symmetry.

DIJKGRAAF: But then it can be false, Paola. So I think you know in this very few people would use that concept anymore because of our whole aesthetic has evolved.


DIJKGRAAF: So how would you-

ANTONELLI: Well it’s interesting-

DIJKGRAAF: …describe what happened?

ANTONELLI: It’s interesting that you say that because at some point in the world of architecture and design nobody said the B word for a while-

DIJKGRAAF: The B word?

ANTONELLI: And people would be scared of the B word. And even now I have a little bit of a hard time talking about it and then I do open the when I have to make statements for instance one statement that I tend to make is that beauty is a sign of respect towards other human beings. But then I switched to aesthetic intention because when we are designers or creatives today we cannot not take into account punk. And I mentioned before Pedro Almodovar, Dada, I mean all the… all of the instances and the parts of and the moments in history that have led us to go well beyond the idea of Platonic beauty. So saying beauty still it leads us to think of the same kind of beauty that your friends mathematicians talk about us like you know this kind of symmetric beauty. So aesthetic intention lets us also take into account you know ugly fruit and and punk and other expressions.  But I do believe that giving, making effort putting effort into the formal aspect of any kind of object is a way to communicate with other human beings. So no matter what whether it’s symmetrical or not it is something that has to be taken into account.

DIJKGRAAF: The fact that these objects correlate so strongly among cultures or something, is it telling us something about ourselves? The fact that we universally are attracted to these objects although we might now have a more complicated relationship to them?

[00:25:06] ANTONELLI: Undoubtedly but there are some cultures and I don’t know enough maybe you know more about this, Annabelle, but like for instance let’s go back to Japan. Isn’t a lack of symmetry praised? A lack of balance, praised? Or not necessarily so?

SELLDORF: Well I think it’s… Certainly that’s my… My understanding of it is that it’s always about the tension of the two, right? And where you put into question the familiarity the formality the… commonality, if you will, of symmetry, with something that puts that into question. I think that’s when that happens.

ANTONELLI: And scientifically, does symmetry create tension or not? Or it’s the killing of all tensions.

DIJKGRAAF: Well I think that the big difference being from the scientific point of view is to look at the symmetry in an object- something which could kind of be boring in the sense you know triangle is something is not the most beautiful object that’s out there. But I think where mathematicians and physicists are going to resonate if you see that’s your theory or something is symmetrical that your theory has- I think it’s almost- I would say it’s almost synonymous with power. It’s the power of understanding things. And one way you can think about symmetry is that it somehow reduces-  there’s an extra amount of order if you look at the- again at the symmetrical object if it’s a round object then you know that in some sense, a lot of the properties of that object are described by its symmetry the fact that you can rotate it around.

DIJKGRAAF: And so it’s symmetry in some sense enhances the power of your ideas or your theories. And that’s actually I think so in that sense this sense of beauty that is used by scientists is perhaps not only just the aesthetic but it comes with in some sense it’s loaded with incredible power of expression and it has in some sense also do I think typically people find an equation beautiful that’s if it’s-

SELLDORF: That’s exactly what you were all saying yesterday.

DIJKGRAAF: It explains a lot with very small number of symbols. And it’s that balance or something.

SELLDORF: Does that not also imply a sense of resolution? I’ve always thought that- that the word resolution is actually a really interesting concept in…

DIJKGRAAF: “Resolution” in which, in which way?

SELLDORF: Well a beautiful equation implies that you perfectly resolve…


SELLDORF: A thesis, right?


SELLDORF: And to that extent, symmetry fulfills that in perhaps a… I’m sort of inept finding the right words right words but it seems to me that there is a sort of elegance about that resolution that may be very satisfactory.

DIJKGRAAF: So perhaps I think you know one explanation can be that scientists are so unashamed the word beauty is that they actually have a different sense of beauty than just that they like something or they would like to display it or something because you know probably the objects themselves are boring. But it’s the power of perhaps me you in the way you could describe that the sort of movement in the art is beautiful because it has been you know so creative and created so much. That might be a different uh-

ANTONELLI: That might be it… because actually when it comes to the formal beauty sometimes they’re a little… they’re a little uncomfortable.. as we were discussing before!

DIJKGRAAF: The B word! I think this might be a good moment to take a few questions.  And what I want to do is just let me put some light on the room. I don’t see anything… but we have microphones! I’ll just stand up… and I want to take a few questions but just raise your hands.  I can’t see anything. Turn the lights on. OK good. Are roving (?) mics here? Ah perfect! Yes, please. I will take a few questions and then present them to the panel. Yes, please go ahead.

Questioner 1: Sure, so uh, I guess through the history of our species what advancements do you think the first straight line gave to our made in sound objects.

All: First straight line…

DIJKGRAAF: Thank you and other questions? Yes, over there, please?

Questioner 2:

My question is symmetry in say, music like harmony and melody or even in occasionally aesthetics, how can you represent that say in other purple means like there is harmony and melody in music for example or even artists like in these paintings that it blends that there’s some sort of a harmony. Is that a kind of symmetry or is there any other way to represent it?

[00:30:23] DIJKGRAAF: Good, it comes back to that theme of proportion. Another question at this point? Yeah there, in the back. Oh yes, you, please!

Questioner 3: So I think Google just released something where they use AI to create art. My question to you is if you were to design algorithm to create art or to not deterministically create art but come up with its own theory of art. How would you do that? What would you do and how would you incorporate symmetry into that?

DIJKGRAAF: Excellent.  

Questioner 3: And I think we often talk about symmetry visually and I’m wondering if we could discuss symmetry through the other senses like feeling or smell or taste?

DIJKGRAAF: One more and then we go back to the panel.

Questioner 4: Uh, in discussions about surgery. There’s  been words like efficiency or even resolution that’s brought up. And one word that I was curious about is the idea of essence in the new design. And I was wondering if there would be an interesting topic for you guys to talk about as well.

DIJKGRAAF: Terrific. Well thank you very much. So are we recharged to conversation. I want to start with the first question but the the first trade line just a little anecdote. I have a colleague of mine and he tells a story, I think he was like six years old, and was in school and the teacher tried to explain some basic geometry and he would draw a line- chalk line- on the blackboard. And he said well this is a line. Now in theory it’s infinitely long and infinitely thin. But clearly that’s not possible. And then my friend raised his hand and he said well you know but in our minds we can think about an infinitely long line. And then I think he was sent out of the class because… poor guy! He became a very successful physicist. But he’s so right. So I want to turn that question around to just… at some point… And I find it still amazing that you know so we can actually even a 6 year old can think of the concept of an infinite long line I think if you think- all of you- if you think about a line a mathematical line going on forever I don’t think nobody of us has a problem with it. Although we know our mind is finite and the world we see is finite. That’s pretty easy to imagine.

SELLDORF: The hardest thing about it is that there’s always a moment when it starts.


SELLDORF: The infinity of it is not as difficult.

DIJKGRAAF: It’s the starting point… but I want to turn it around, I mean in some sense it’s almost going back to Plato and these images so it’s easy to think about a circle we think about the circle. So both you wouldn’t— How does that– and we don’t know when we first thought about these. But clearly it’s very easy to think of these concepts. What is the role of these kind of mental almost mathematical concepts and the actual say in architecture is that somehow- does it play a role or mean it’s clearly attention we don’t– But how does that change our view of the world?

SELLDORF: Well I think it’s a perpetual change, right? As we become familiar with concepts generally talked about as a learning.  We can develop and evolve our way of thinking. I mean to me, the question of a straight line is actually a really interesting one because it’s the difference perhaps it’s that we think a straight line is the opposite of an organic line or an organic… shape.

DIJKGRAAF: Because it’s- we don’t see them in real life. I mean if you’re walking through the jungle there are very few straight lines.

SELLDORF: Well except that you do where gravity plays a role. Right. Like if you- a spider drops. A- a thing. (laughs) That’s right. It goes down in a straight line and and I think our experience of straightness is actually something that is very profound and very old, perhaps. I don’t know where it started.

DIJKGRAAF: Paola too, what are your thoughts about this?

ANTONELLI: I think that we’ve always been able to imagine a straight line but it’s been really hard to make it happen. Like we always know what we want but our tools are imperfect. There’s a great exhibition that is open right now in Milan that is called the prehistory of design which shows something that I’ve always believed that design started when we made our first tools and then it goes all the way to today and there’s some AI ideas- it’s really beautiful. But so there’s not much distance between the first spear and the AI object. It’s just that we’ve been laboring for so many centuries to get better tools to get there. So that’s really the point.

[00:35:34] DIJKGRAAF: You feel it in some sense when people were making these first tools that these mental concepts of… almost mathematical concepts that are in our mind were guiding them? Is there some sense of empowerment when you make something which is-

SELLDORF: Definitely!

DIJKGRAAF: –close to this Platonic image?

SELLDORF: Um, or close to something instead that is completely non-platonic and that is not even Euclidean because you’ve gone through the different steps in history that led you to believe that the goal is not anymore the Platonic line or the Platonic idea. So we- we follow our destiny. We develop and mature and make our mistakes as humanity all together. And- at every single moment we have an idea of what we want to do and we have this eternal frustration of not being able to make it exactly the way we want because our tools are imperfect. So that’s the tension that I feel exists.

DIJKGRAAF: Well I think that I mean it’s something that I have to say something about because indeed you know it’s kind of amazing that with all the examples all the pictures we show anything we point out that we think it’s a symmetrical object it’s not because if you look close it’s not. These exhibitions, the coils?

SELLDORF: Nothing.

DIJKGRAAF: They’re not really symmetric. They remind us of these images. And I think nobody can point out a perfect square or perfect circle. If you look up close you see little bumps. You know it’s always… so we have to work and live with these kinds of failures.

SELLDORF: But that’s only if the concept of failure is is interesting. Yeah that because. I think. In the first place we think of it as a concept. And it is similar to being able to thinking about the infinite line as if you can think of a perfect square that gets you a long way. At least prime architect.

DIJKGRAAF: Yes. I want to come back to a sort of second theme that was mentioned by the audience which is indeed the fact that we kind of- very one dimensional in the sense we have been really talking about visual experience. While I think you know in the arts and just the way we relate to the world it’s different. Music was mentioned in fact again from a scientific point of view. If you look at the power of symmetry so well there’s power. We think of symmetry as movement… turning something around or making inverting it or shifting it. But in fact another way to actively do something with an object is moving it in time. And the way the nature is for instance invariant under translation to time and the fact that the laws of nature do not change minute by minute. In fact we think they are eternal. It is a very powerful principle again in physics something that we find “beautiful”. And music was mentioned where of course you experience in many ways the same kind of patterns that you see in design. There was the suggestion what about the other senses. Is there any problem you want to try to dare to step in this kind of multisensual experience of– design art?

ANTONELLI: It’s so huge!  So several years ago together with a collaborator a colleague of mine Jim Hunt We did a symposium at Parsons that was called Headspace. and he was about-

DIJKGRAAF: Headspace?

ANTONELLI: Headspace is a technology that is used in the perfume industry to capture the scent of living beings without damaging them. So usually you do it with camellias and- well.

SELLDORF: Sorry, you have to explain that again.

[00:39:25] ANTONELLI: So! It’s to capture molecules of scent from things, from objects, from flowers without damaging them. What it- it’s almost like a cupping like you know when you do cupping in Chinese acupuncture and then it’s connected to machinery that uses spectrometers, so you replicate the molecule and then you and then you replicate them. So it’s called headspace technology so we called it Headspace. And he was about scent as a form of design. So we had a whole day long of architects and all of these great perfumers. But the interesting thing is that we assigned some perfumers from IFF which is international flavors and fragrances so they usually work for like MS or like you know they work for big companies. And we assign them with some architects to create custom made scent. And one in particular a team of two great perfumers- French- like French perfumers like– with those noses- were assigned to Majora Carter. That’s an activist friend of mine from the Bronx to create the perfect scent of the South Bronx. So it was fantastic. They were like these videos that were hilarious of them arriving in Lima or in the South Bronx who was just so funny. But everybody enjoys it tremendously.

But what I learned from that experience is that of course we tend to never think of a scent that way but it’s an algorithm. It’s a composition of different molecules and these big fragrance companies of course generate all sorts of artificial fragrances but then there are some molecules that they develop and patent that are the most expensive ones, the ones that get them millions, that exist only to enhance and create a lack of symmetry like you know just create the tension that you were discussing before between other molecules. So what I’ve come to discover is that sense both in static and in dynamic terms the way it starts and it has a head and a tail blah blah blah, like whisky, is really about the evolution in time and it’s about creating the tension that is, in my ignorant mind, non symmetrical. But then you know sometimes when you talk about the symmetry in music that develops over time I’m a little lost and maybe there’s a symmetry also to scent.  But definitely non-symmetry seems more interesting to so many perfumers.

DIJKGRAAF: One association I immediately have is that because- scent is such a refined notion because it actually acts of the individual molecules. Right? I mean it has so many dimensions to bitboard (?) and just say sound or something in fact these molecules are all… you know are… very very kind of usually asymmetric. So if you take the mirror image of these molecules you will actually- they won’t produce- you get something completely different. Annabelle, for you I was also thinking in terms of–

SELLDORF: I– I just wanted to say that…

DIJKGRAAF: Yes, please.

SELLDORF: I read somewhere that…. As a thesis that symmetry represents… defying memory whereas asymmetry supports memory.

ANTONELLI: Ah, interesting!

SELLDORF: And I think that’s really interesting in that particular instance especially because-

DIJKGRAAF: So you mean that an asymmetrical object remember it because it’s like-

SELLDORF: Asymmetrical. And so I mean I concluded from that that that comes to be because it’s more individual and incomparable to something that is immediately understandable. But that certainly with respect to sound makes a lot of sense.

DIJKGRAAF: I want to ask you in terms of architecture and buildings- what are the other senses or something that are part of the experience of building? It’s not only the visual.  

SELLDORF: Well, I think. Tactility… and… scent a little bit… but touch.


SELLDORF: Oh I guess tactility in touch. Same thing.

DIJKGRAAF: Sound, perhaps?

SELLDORF: Sound of course sound I think is incredibly important. And reverberation I think that is different from music and most music is written and therefore this sort of idea of some symmetry in music makes some sense to me because it can occur as part of repetition or it’s a sort of translation of the visual into something else whereas… mere sound… I don’t know if that’s symmetrical.

DIJKGRAAF: Connected to that question: the concept of harmony was brought up and we already talked about balance and harmony. Harmony I think might be a similar “the H-word” or something not sure… Uh our concept that you know have had a very Platonic beginning and kind of evolved. I think that you are entitled in our discussion of symmetry to kind of move in that direction. I think that’s all I want to talk a little bit about the concept of balance and harmony and… which I think goes beyond symmetry is something but it’s… Annabelle you mentioned proportions. Of course there’s a long standing tradition also to kind of try to capture these proportions in numbers in mathematical numbers- there are famous numbers out of… ancient time and the golden ratio and various ways in which the mathematical formula has tried to capture these notions of balance and harmony.   You feel that we’ve talked about kind of symmetry as kind of evolving… it’s no longer our platonic goal and a lot of it is about attention with it. Is balance and harmony still in architecture? And perhaps in your work? Is it something you strive for and if so how do you capture it?

[00:45:49] SELLDORF: Well that’s a big one. I remember reading. An article a long time ago where Ren Coalhouse (?) has said that striving for brutality in architecture was a very important concept. And-

DIJKGRAAF: Is brutality the opposite of harmony?

SELLDORF: Well it’s- in a sense I think it is. And-

DIJKGRAAF: Unbalance.

SELLDORF: …Right, exactly the lack of balance. And… I struggled with that statement then, and I do today. Because I actually think there is plenty of lack of balance and lack of harmony in our lives as it is. So, providing the opposite providing a kind of… meditational quiet is something that I think is desirable. Having said that, it can’t happen without tension, it can’t happen if it’s not held in a..  I don’t know precious– precious separation or something like that. So… right, (laughing) I do strive for harmony.

DIJKGRAAF: This concept of balance and disproportion are something which can be kind of almost like calculated? You think is there some kind of artist or the laws there. Is there some order in what makes something balanced or not that its evolving or independent?

SELLDORF: The minute that there are laws and order then it’s predictable. And I think that is what would disrupt the idea of harmony are bounds. I think… you see when you experience a beautiful proportion you immediately have a sense of balance or a sense of well-being and that is not a bad thing. But I think it’s too simple to say that that’s all there is. You can’t, you know, it can’t come to perfection so to speak, if it’s not held by something else. Does that make sense?

ANTONELLI: Yeah I was thinking that. All the designers that I know from furniture designers to visualization designers. Nobody thinks of balance and harmony.


ANTONELLI: No, not anybody that I can think of. The goals are different. And you know design-

DIJKGRAAF: So what happened there? At some point in the history of design–

ANTONELLI: I’m not sure that it was ever the goal for design- many people argue that design was born with the industrial revolution as I mentioned to you before it was to me much, much older than that.  But harmony maybe can happen, can be important in some ritualistic tools. Right? So you were talking before about the meditative spaces so there are some tools that are meant to. But they’re- the goal is harmony because the goal of their use is harmony, you know what I’m saying? So for these particular objects, then it’s important. Otherwise I’m thinking of furniture designers right now some deals want to have comfort. Others want to have the demonstration of a new technology that enables one to make knots and slowly defy them in a chair so the goals are different, and hardly ever are the goals harmony for the sake of it.

DIJKGRAAF: I mean in some sense yes, Annabelle?

SELLDORF: Yeah- I think again similar to the work of symmetry, it doesn’t describe the objective. That may be– it may be an inherent goal to try to strive for harmony because the intelligence of the act of making a particular object includes that. But I think that it’s not solely that right?

ANTONELLI: No! I agree.

[00:50:13] DIJKGRAAF: Since we have several times where we mentioned the fact that perhaps a much more interesting topic is asymmetry. The fact that it is tension with. And I think there’s a long tradition there too. I mean I think we have some images of these kind of wonderful Islamic art tilings you know where you… and it’s actually quite lovely. They are for instance in Alhambra (?) you see these wonderful tilings and I think they were done in a kind of experimental fashion! Designers trying to find all possible patterns and mathematicians now know it. That’s one useful fact for all of you to take home that are exactly 17 different colorful paper patterns. If you try to build a different kind of wallpaper patterns and I think all 17 are you can find them. But I think there is the use of the phenomenon that these decorations are done in an almost perfect way because there’s always a small way in which it is deviating.

DIJKGRAAF: You have to tweak it for, uh. So what is our fascination with that kind of asymmetry-

ANTONELLI: With cheating?

DIJKGRAAF: The cheating, just yes.  

ANTONELLI: Oh well, we always like to cheat. I don’t know what that fascination is, but I was thinking that even- one of the most symmetrical pieces of design is a bean bag chair, which is my favorite piece of furniture. Right? But it starts as symmetrical in order to accommodate any kind of asymmetry.

DIJKGRAAF: Ah. So you think of the beanbag lying there as a perfect sphere.

ANTONELLI: Yeah yeah. And so I think that we love cheating. There’s nothing better when you’re creating something that’s to start with a ruler and then start seeing what happens when you start cheating.

DIJKGRAAF: Yes. So, why?

ANTONELLI: Well because I think that’s creativity, right? I I don’t think of creativity as a process that is about following the rules that I don’t mean I don’t even want to romanticize breaking the rules. It’s not something that has to do with an infantile position. But it’s really about finding new paths every moment.

DIJKGRAAF: Do you think then again going back to the symmetry perhaps also as kind of a metaphor for a very ordered and organized world that we need that some sense as a background in order to-

ANTONELLI: Definitely!

DIJKGRAAF: –making our very mean in some sense are we talking about variations on kind of a theme that is by itself perhaps kind of boring and discarded.

ANTONELLI: It’s like fighting against your father or mother in order to grow. You know, it’s like one of the rules. That’s why the question about the algorithm was also incredibly interesting because yesterday after hearing the panel that you were part of after hearing all the scientists talk about the symmetry equations. I went home and I started thinking of the symmetry in algorithm. Algorithms are not symmetrical. They are recipes that are just starters for sometimes unpredictable evolutions. And I was trying to think whether the algorithm is the opposite of the equation in this idea of symmetry and asymmetry. So I’m asking you what do you think.

DIJKGRAAF: Well it’s quite interesting to ask about kind of symmetry in kind of equations because you know I love to say that if you have an equation, you know to most- which typically looks something like A equals B or something-

ANTONELLI: Well yeah, kind of… (laughing)

DIJKGRAAF: Usually not enough attention is given to the equal sign you know because it’s like always about A and B.

ANTONELLI: You’re so right.

DIJKGRAAF: And the equal sign, I love it. It’s actually perfectly symmetric and I always think of it as a double chord cable connecting a and b and it’s connects A to B but also connects B to A. And if you take some of the most powerful equations in physics… so I think perhaps the most famous equations is E=mc squared, Einstein’s equation. So what does it tell us? It tells us energy on the one hand equals up to some concept of proportionality, c squared, equals mass. So what does that mean you can take an energy, pure energy, and turn into mass. You can create particles out of pure energy. And the other way you can take particles and for instance should do in a nuclear explosion take mass and produce into energy. So it somehow takes two concepts that were not connected… it equates them but it also it connects them, it produces a kind of a nice left right symmetry which in many ways…

And I think that’s why we call it beautiful. Why is it beautiful, because it’s enlarges our world. It connects two parts that didn’t even need to be together and now there’s A and B there were from different worlds in order to get the simple equation effect there’s this nice connecting piece of equal sign that actually makes them talk to each other.  So there is… and I think that’s almost like a.. I think perhaps if you think about it you know the deepest development perhaps in mathematics has been over the last hundred, 200 years that instead of looking at objects I think mathematics tend to be- used to be- you look at different objects. The modern way of looking at mathematics all the objects are just the beginning. The question is, what are their relations? How can you go from one to the other.

[00:55:53] ANTONELLI: It sounds like you’re talking about design.

DIJKGRAAF: And what is the relation? And so what mathematicians came up with is a whole framework to think about is so are rhetorical category theory and it means that if you and that’s why symmetry came back. Because if you have object you say well you have a square you have a triangle. But it’s like no, wait a moment. How can we relate these two, how can we relate a triangle to itself? Well for instance by rotating it over a hundred twenty degrees. So the symmetry is actually in terms of the relation of objects to each other not to the object per se. And I think that it’s in some sense a liberating view and I think it’s very much connected to the theme that you were talking about too, it’s not so much about individual even pieces of design or architecture it’s how do we relate to it and somehow having a much more connective view of the world where it’s not only about the dots but the various lines connecting the cells. Your question about algorithm is fascinating. I don’t know whether-

ANTONELLI: Somebody’s question here was really good.

DIJKGRAAF: And then it the way I view the question also is that while suppose we- and now I’m really jumping into the deep- but that we are no clearly our lives are changing through science and technology. You know we we’ve been talking something about concepts that date from the old Greeks. These are 25 year hundred old concepts. But if you go to the here and now, where science and technology is taking such an important role where in many ways even thinking is machine assistance- we are no longer it’s not just a single human being it’s human beings connected to each other as human beings connected to machines. Artificial intelligence will pay more and more an important role. I think- certainly I know science will not stop and I remember this kind of famous moment when a guy Kasparov was first beaten by the chess computer Deep Blue. They said well is this the end of chess. He said no no no. From now on it’s me and the machine against anybody else.

So it’s like this. No, we we are embracing. We can’t think about science anymore without all our instruments, our computers, everything that’s happening there. What happens if you just be bold and try to look at the future? And I think that that’s where the question was hinting at. Where algorithms combine with human efforts, will probably make design… what you see?

ANTONELLI: That’s already happening. I see it more and more as I was mentioning before this idea that so many architects and designers are trying to grow objects instead of making them from the top down is based on the idea of algorithm. I don’t know whether an algorithm can create art because I don’t know what art is but I know that there are artists that are doing so all the time.

DIJKGRAAF: If the algorithms sells its art, is it like–

ANTONELLI: I just– that’s the big question.

SELLDORF: She wants to go there, she wants to do it….

ANTONELLI: …I always say I deal with design…

SELLDORF: …She wants to talk about it…

ANTONELLI: But but that’s happening already all the time it’s happening in the digital space, it’s happening on paper, it’s happening in the 3-D world, and in the 5-D world. So it’s already-

DIJKGRAAF: What’s the 5-D world?

ANTONELLI: 5-D world, you know, 5-D… What is used in by some production designers as a world building idea. So the 5-D conference was created- well because it’s in the digital space but it’s definitely about world building. There’s architecture in it. So it’s Alex McDowell that was the production designer from Minority Report that coined it first and he had created this great conference that was basically all architects and special effects people and it was about the idea of building worlds based on not only special effects and spatial savvy but also on narrative and game.

SELLDORF: Game technology…

ANTONELLI: Yes, so it’s already happening a lot when it comes to our space. You can talk about architecture also-

[01:00:00] DIJKGRAAF: Well, tell us what’s happening and where are we heading?

SELLDORF: A lot of- I’m-

DIJKGRAAF: Small questions.

SELLDORF: …pretty much the last person who knows where we’re headed. I think architecture as I practice it is on its last leg. But what I  think is-

DIJKGRAAF: Last leg?

SELLDORF: …Technically…

ANTONELLI: I don’t think so. I think that people will always need spaces where they feel comfortable…

SELLDORF: What I’m very interested in is that the way we get there is different. Many young architects and as they are graduating, are becoming interested in game technology. And I think that’s a fantastic thing because it adds a dynamic to how we think about urban space and architectural space that we haven’t really fully grappled. Ultimately I think everything happens at a moment where somebody needs to make a decision. It’s not that algorithms are going to decide whether something is art or not. Maybe it will be the two of us either- or the three of us. But the decision in the conversation lies with the people. So how we use our tools and how we advance to another level. And I think that is the fifth dimension that you were talking about.

DIJKGRAAF: What I find fascinating I think if you look at what’s happening in the world of science and again I think we’re going through the same kind of transition in the sense that I would say in the old days we were basically looking at nature and studying nature and looking at what are the natural objects that we find. Biologists would study all kind of organisms. Geologists would go around and find all kinds of rocks and look at crystal structures etc. Now as we understand the building blocks both matter and all living matter it’s no more about understanding the objects that are around us. But no no no we are studying the space of all possible objects.

SELLDORF: Exactly.

DIJKGRAAF: …Which is vastly superior I mean I think Richard Dawkins made this point that if you look at every object and every organism ever lived on planet Earth. And look even on the kind of DNA code that came with all these organisms. That’s a totally marginal fraction of all possible DNA. So each of us are extremely lucky because we are the one design that actually was executed and it was actually produced with this mental space. And I think we are in both in the life sciences with synthetic biology and in the, say the study of materials in terms of nano-tools or nanotechnology. We’re just beginning to explore that space. And I think we have- we need a completely different framework to approach that space because you can’t do just everything. You have to find your way through this infinite space of possibilities which is much more of course where design than art is. The moment you take your pen and you put it on paper you’re already drawing something that nobody has drawn before.

ANTONELLI: Very true, and why are there such great collaborations that have been happening for the past eight almost 10 years between synthetic biologists and other scientists and designers. It’s really fascinating.

DIJKGRAAF: Let me phrase it like this- is there anything that the scientific world has to learn from the world design and architecture to kind of deal with that kind of infinitude of possibility.

ANTONELLI: Of  course and it’s already happening and it’s not really like learning it’s about collaborating. There’s been one of the schools that in the past has done the most is the Royal College of Art in London. There used to be this course called design interactions. It was a name but in true it was speculative design. So the designers they were all graduate students and they were-

DIJKGRAAF: What’s speculative design?

ANTONELLI: It’s about what if, so speculative design-


ANTONELLI: What if. Speculative design is about building scenarios that are usually based on objects that talk about the possible consequences tomorrow of our choices of today. So they would work especially with the scientists at Imperial College because they were around the corner. But to give you… to give an example- one of my favorite objects was this menstruation machine. So it was a contraption that enabled men or other non-menstruating beings to really experience menstruation with the cramps….

SELLDORF: Lucky them.

ANTONELLI: Yeah exactly. So that was an example of an object… Or another year there was a beautiful collaboration with another highly experimental school of design that does biology that is in Perth at UWA. So in Perth they have developed- they were among the ones that had developed in-vitro meat. And in London the designers were thinking of the steak of tomorrow like if you can develop meat in vitro what should a steak look like. So this collaboration and also there’s another designer Daisy Ginsburg that’s been working a lot with Drew Andy who is a synthetic biologist at Stanford University, so it’s beautiful… beautiful to see what kind of collaborations–

DIJKGRAAF: You used the B word!

[01:05:46] ANTONELLI: Oh yeah, the B word! (laughs) The collaborations that are happening between scientists and designers are fantastic and I think that the reason why designers want to work with scientists it’s a no brainer. But scientists were initially diffident but now love it because when they’re working with designers they can get out a little bit of the peer review system that makes sense and time timid. You know, nobody will think of these projects as replicable, as scientifically accurate. They are speculative, once again, and I don’t think that scientists speculate enough.

DIJKGRAAF: Well I’m a string theorist, so…

ANTONELLI: So hopefully you’re Mr. Speculation! (laughs)

SELLDORF: Well I was just thinking that there there are some very directly applicable areas where science comes together with design and architecture and that is lighting.

DIJKGRAAF: Lighting?

SELLDORF: Yes. I mean we perpetually look for new ways to improve artificial lighting- it would be great to improve on this. But for example there is this Italian scientist who just came up with a technology to create light as we truly experience it. It’s an LED based system- I should be able to describe it better than I can- but it’s essentially offering the possibility to create natural light artificially. And it’s fascinating because if that really happens you can build skylights in your basement. And if you think about the possibilities that that is going to have for the built environment it is strictly amazing.

DIJKGRAAF: So I think you’re already swallowing your words over the last leg that you’re standing on, because it looks like the beginning of an exciting story. I want to give the audience one more opportunity… so we’re gonna struggle with the lights. We’ll try to bring them on and do another round of questions. We do manage to do that. Think about questions and raise your hands.  Anything.

ANTONELLI: You’ve been so good so far with the questions.

DIJKGRAAF: Yes. One more, yes.

Questioner 5:One would think of the extroverted representations, physical representations in the world the arts, architecture as a reflection of the brain itself. And how do you think of symmetry in the sense of the representation of our minds and its manifestation in the world then and how that kind of feedback loop happens? I know this is kind of a vague question but I’m trying to maybe think of how our minds play a role in…

DIJKGRAAF: It’s a good question- the brain and the mind. Other questions here…? Could be be quite general about the interplay of science and art… over there?

Questioner 6: I’m sorry it’s the same question- similar question they asked last time I was just thinking that you have a straight line and in a sound like suppose… would a constant sound be a straight line? And what would be a sound that is like a circle like a sound that repeats itself? And can you add them to get like a cylinder or in a pyramid like this you know going on that part of how you represent different… similar like, symmetries mentally.

DIJKGRAAF: OK. So that’s a question over there?

Questioner 7: Thanks. I remember you mentioning earlier about this 5-D thing. Could you elaborate on that? I guess?

DIJKGRAAF: You want to understand where the 5 comes from in that, a better definition, good. Any other questions? Yes.

Questioner 8: So what would you think, and this is probably an interaction of physics and symmetry, if there was an absence of physics or physical laws? How would that change the idea of symmetry and what you would define as symmetry.

[01:10:11] DIJKGRAAF: Interesting question. And one more and last one there in the back.

Questioner 9: This is kind of a weird question but when I think of symmetry I think of like infinite fractals and like infinite structures. Do you think symmetry would exist without like infinity and like you think because with like most observatory things being finite do you think like, how do you think we can understand infinity necessarily.

DIJKGRAAF: Good question. OK I’ll turn back to our distinguished panel.

ANTONELLI: (jokingly) Very distinguished.

DIJKGRAAF: Paola I think we’re all still confused about the definition of 5-D.

ANTONELLI: And I don’t want to say something wrong so I think the best would be to go to the Web site and see. I can describe what it was without giving a definition. So when it was founded the first time, this 5-D institute was the idea to have the three dimensions of the space plus time plus also the idea of all the different parallel lives and worlds that you can have in a video game as Annabelle rightly pointed out, and in a space that is connected digital and physical. So it was a way to think of the worlds that one can build in the digital space and connecting them also to the physical world.


So what Alex McDowell did is he founded this conference where as I mentioned to you was like video game designer special effects people and architects because there’s really a need for architectural savvy in the digital space. And then now he has an institute at the University of Southern California it’s called world building in which he uses people that do special effects and that do gaming and then architecture students and also urban design students and they apply their skills to the resolution of instances like… there’s Makoko that is an area in Lagos, Nigeria that is all on stilts that is on the water and they’re trying to use the world building institute skills so architecture plus urban design plus the ability to create whole worlds and narratives in the digital space to address issues in that particular location.

So I know that I haven’t answered the perfect definition and I’m doing that… I’m not answering in order not to do injustice to the concept. So if you don’t mind looking it up later on the 5-D conference and 5-D institute and I expect that will you find there the perfect definition. But it’s really practicing architecture and urban planning using all the tools at our disposals today in a particular way.

DIJKGRAAF: Great thank you. And also I feel perhaps that we should answer the question about music because it was asked twice. So one way to think about the symmetries in music they have to do with the symmetries in time but actually a convenient way to think about it- to think about the way the music is written. In the music score. So you can think of a music score essentially as a band of music and you can see certain patterns. For instance if you have a repeating phrase it looks almost like one of these kind of beautiful tilings that we saw behind us or friezes as they are used in architecture…

SELLDORF: Well if you look at the music written by Bach…


SELLDORF: That’s incredibly interesting because it’s an intensely visual experience of sound. But… anyway sorry-

DIJKGRAAF: No you’re totally right and I think sometimes these kind of scores they use beautiful…. They look beautiful. I mean they have actually these symmetries you see them repeating- not quite the same. Sometimes you see inversions sort of reflection symmetry could there be too. Literally was a trick in composing to take a phrase and just kind of turn it around upside down essentially and actually to think about it. It’s perhaps you know if you think about the circle, I said to you it is very difficult to see circles in real life but in some sense they are often rare around us because as soon as you have something that’s periodic something goes up and down can be as a tone, a musical note, but it could be anything it could basically be the movement of the sun and the planets.

So of course they are moving orbits that to great precision are circles. And so in some sense anything that this periodic in life. And if you think about it almost everything is in some sense an expression of symmetry because it’s repeating itself in the same way as a checkerboard pattern or friezes repeating itself. So if you think about it that way invariance under movements in time are all around us and in some sense it’s perhaps a more even more you know I think deeply engrained experience in our brain to have something that comes and returns because as you know every day comes and goes and many of our experience… so there’s a lot of symmetry in our lives and-

[01:15:55] ANTONELLI: I wonder if we can apply this also to coding. I’m thinking there’s a beautiful visualization that Ben Fry, he’s a great visualization designer, did of the Pac-Man code. He visualizing almost looks like music so you see the different code and then he literally showed where the code says go back to and reiterate and-

DIJKGRAAF: So we see the same kind of visual-  you can…


DIJKGRAAF: And that is a great way to… in some sense… use kind of our different senses are related to and expresses.

ANTONELLI: In all of those cases it seems that repetition is an important aspect.

DIJKGRAAF: Yes. Yes that’s true. And will someone to go to the question about fractals? And it’s a very, I mean I think most of you know fractals that have this concept that if you zoom in they are the same or at least is a variation on something. So it has this fascinating concept of infinity because you can zoom zoom in zoom in. It kind of never stops. The kind of concept of symmetry that’s involved there is a deeper kind of symmetry, symmetry that I want both of you to reflect upon which is the symmetry of a different kind of motion. It’s the motion of zooming in or zooming out. So it’s different from going to the left or- so think about you have a picture or you can shift it you can rotate it you can reflect it but it can also zoom in and zoom out and it has to do again with skill- the very skills over which we see things. A fractal is amazing because it’s the equivalent of this mental image of an infinite long line that goes on and on all the checkerboard pattern that goes on and on it’s perfectly symmetric of course a real checkerboard will not…. and but Paola can you say something about this concept of skill and the way we think of invariance and the scaling but perhaps also breaking that symmetry.

ANTONELLI: Absolutely.

DIJKGRAAF: Because I think that’s an important element in design.

ANTONELLI: You’d be amazed how much people in the design and architectural world know about scale because there is them not only because of that but there is a very famous movie by Charles and Ray Eames, the Powers of Ten. So it’s something that every architecture and design person-

DIJKGRAAF: Every scientist…

ANTONELLI: Yeah, it’s so great.

DIJKGRAAF: Please look at it online and it’s a 10 minute movie and it captures basically everything we know about nature…

ANTONELLI: I know! It’s amazing.

DIJKGRAAF: …and it’s perfectly executed and…


DIJKGRAAF: …and design.

ANTONELLI: And I’m also going to make you smile because my thesis was entitled “Fractal Architecture” and it was this idea that by having- by overlaying- a digital space and mixing it with the physical we can really go through scales of a very different kind of architecture so I think it’s happening a lot. There was- there are two architects Ben Aranda and Chris Lacsh that published a pamphlet, a Princeton architectural pamphlet, in I think it was 2007 that was all about all the different stratagems that one can use in parametric architecture to build. So there was tiling there was pyrolling (?) and so on and so forth. And in a way it was an attempt to take fractal geometry and distill it into laws that could be applied to architecture and then build by computer. So it’s something that is absolutely… that is very much used by architects and also by urban planners. There’s been a lot of scale study that moved away from simply the building and went to the city the territory the nation and computers have helped us once again make this jump in scale.

DIJKGRAAF: I want to say something to the powers of 10, it’s beautiful but it actually dates, and this by Dutch pride, it was a Dutch physicist who later became an educator and casebook and he first thought of this powers of 10. It’s a beautiful book. It’s the same thing it’s like it’s actually an image of a woman sitting with a baby in a in a young child in a garden or somewhere in the middle of the Netherlands and then he zooms in and zooms out. But what I loved is that he created this school, the (?). And it was an experimental school and he wanted to explain the notion of scale to children. And the first design thing they had to do is to draw a brick. On a one to one scale. Now the thing is that we all have drawn a brick you know, we’ve drawn a house, we’ve drawn a brick. I’ve never drawn a brick on a one to one scale because it’s big, you know? So the first thing I had to do is to draw this large brick and it’s actually one on one! It’s very rare if you draw anything. Well, perhaps if you draw your hand- it’s like… every child has done that. And so for him it was not only to think in these different skills but also to kind of ground you at the one to one scale which is actually in some sense I find it kind of a lovely image because it really–

[01:21:21] ANTONELLI: It truly is! And the funny thing is that now with virtual reality you can put yourself in the architecture and perceive it as one to one. Even though you’re the one that’s not one any more. Or you are whatever you are. But it really… it really is happening.

SELLDORF: And I think that’s also there is danger with that because I think the-

DIJKGRAAF: Danger with what?

SELLDORF: With the ability of putting ourselves onto multiple scales, the loss of the experience of what you just described is magnified.  I think I observed that anyway in as a practicing architect that the direct understanding that happened at one time through drawing by hand experience of the dimension is becomes more and more remote and becomes more and more theoretical and as it becomes theoretical it moves away from us. This is obviously a sort of… old fashioned argument. And I think that we need to actually find a way to do both. Of having the sort of immediacy and tactility of how thick is your shirt, how tall is your seat, how large are your feet, how big is a brick? To… what is the dimension of the house, the city, town or the country or whatever. And how to negotiate that I think is immensely difficult. And I feel like we have a lot of ways to go to tackle that.

ANTONELLI: So you don’t think that a new means of reproduction like, you know, virtual reality helps?

SELLDORF: Well they do and they don’t. I think it’s a little bit of both. I mean we are enabled in ways that are mind boggling. And at the same time I notice how people lose the direct touch with that dimension. And I mean very specifically dimension. It’s just an observation you make because we’re so focused on the vast amount of things that we can do.  That the very close understanding of that dimension is difficult to grapple with.

DIJKGRAAF: So it’s a fascinating theme that we are going through all these kinds of transitions. And though we talk about the concept I was thinking on the concept that we talked about today which is the naive beauty of symmetry etc. is something that probably could have talked to somebody who lived 2000 to 4000 years ago or something. It’s not a new topic or something. On the other hand you know particularly though both the world and science and art has gone through these spectacular developments so it’s come up and I just said no we are probably really only at the beginning of what’s going on because our technology will completely change the way we approach the the both of these fields.

And so I want to ask you both to speculate on the kind of discussion that we’re having right now is that a discussion that we’ll keep on having? That kind of tension? Because one thing I kind of picked up in basically everything that you said both of you said is that you know there is these are these mental images or these beautiful concepts platonic images which create this kind of tension. What what we want to create and how the world that we want to live in, is that something that will kind of stay with us or is this a subject that at some point it’s kind of… over and out?

[01:25:36] ANTONELLI: I believe it’ll stay with us. I believe we’ll always feel inadequate we’ll always feel that we want to do better. It’s in human nature I hope that we will keep having this discussion over and over. Of course the context will change, the tools will change, but we will always want more.

DIJKGRAAF: What is the essence, then? What is the essence of that tension?  

ANTONELLI: I think the essence of the tension is never being able to reach the ultimate goal whether it’s perfection or whether it’s saving the environment but being better than we are it’s always like we always have a carrot in front of us.

DIJKGRAAF: Just chasing that Platonic image.

ANTONELLI: Not Platonic! Platonic images don’t do that much for me anymore. It’s just chasing the image of what that ‘better’ would be.  You know, and maybe it’s completely not Platonic. Maybe it’s brutal, you know and-

DIJKGRAAF: So you say the actual concept of this perfection is changing and-

ANTONELLI: The concept of the unattainable. You know there’s always something more. And I was watching the other day. There’s a  British woman that I love so much she’s done a lot of body modification she’s done. Also the eye balls tattoo where you become the white or the eye becomes like bright blue. And so I just went I started browsing all these body modifications that happen because I didn’t know much about it. It’s amazing what some human beings put themselves through to achieve whatever image they have. That is definitely not platonic. Of what it is that they want to achieve. So I think that that’s a metaphor for all of us…

DIJKGRAAF: … for the struggle…

ANTONELLI: Whatever, we will keep on struggling for something more and beyond.

DIJKGRAAF: Yes. Annabelle can you relate to that?

SELLDORF: I happened to read the New York Times book section this weekend and there was an article about a German man who was born with very limited means and he became fascinating to people because he was unbelievably capable in the course of his life he -who not only fathered 14 children and had multiple wives who he outlived, but he was capable of making these incredibly sophisticated…. Like, true miniature` manuscripts. And there is an exhibition now, I can’t remember where of all of the works that he did. And why was I thinking of that? Because you were talking now and earlier about our inability to create the perfect tools. And while I think that there’s this infinite struggle of course goes on.  But I think in my mind the tension comes from the achieving, from the Eureka moment, to the having to push the envelope to the next thing. And I think that if there wasn’t a very once in a while the sort of elated moment of saying we did achieve if not perfection something that’s very if we couldn’t experience the pleasure of the experience of nature or the pleasure of experiencing art in its purest way whatever that may be. I think we wouldn’t be able to go to struggle from the next thing.

ANTONELLI: By the way it was at the MET, that exhibition.

SELLDORF: Well yeah, that’s right… I really want to see that show!

DIJKGRAAF: I think that’s actually, taking both your points of view together, it’s kind of fuel we’re kind of approaching the perfect end to this Salon because what I take away from this is that you know we’re kind of placed in between this kind of world of perfection and symmetry and asymmetry and the chaos is like this kind of perfect place where we as human beings can define ourselves as struggling to try to reach a certain goal which we never reach. But you know we have this great gift that there’s so much order around us that makes it possible. So I think I think in terms of that challenge…

Both: (laughter)


[01:30:14] ANTONELLI: No I was looking at the image. Yeah, pretty much. (laughs)

DIJKGRAAF: Yeah, it’s pretty- actually it really captured it all… I think that might be the feeling the audience has when they’re following our dialogue. But I just want to thank both of you because clearly this was a grand topic. It could go any way and I think in the same way we do say that you know we are struggling to do the impossible. I think both of you did. I think you did it very successfully. Think. And thank you so much for enlightening us with your ideas.

Big Ideas
The Beauty of Balance

Why are we drawn to symmetry? Because it provides order in a seemingly chaotic world? Because our brains are the product of the very same laws that yield the flower, the snowflake and the solar system? Because evolution selects for structures with symmetry? In this Salon, we will ask an interdisciplinary gathering of artists and scientists to explore the pervasiveness of symmetry throughout our study and appreciation of the natural world. This program is part of the Big Ideas Series, made possible with support from the John Templeton Foundation.Learn More

View Additional Video Information

Up Next

1,647,782 views | 01:36:02
132,170 views | 00:57:27
1,317,215 views | 01:30:08
51,448 views | 01:27:46
56,184 views | 01:25:38
2,565,678 views | 01:29:37
66,085 views | 01:24:01
1,255,694 views | 01:29:11
1,231,138 views | 0122:24
71,164 views | 00:32:32
1,444,727 views | 1:11:33
5,130,394 views | 01:24:38
2,457,849 views | 01:27:24
3,862,253 views | 1:17:46
1,467,757 views | 1:00:10
107,797 views | 00:57:28
1,566,584 views | 01:00:35
1,052,690 views | 01:02:39
84,564 views | 00:41:54
1,390,398 views | 00:59:56
67,091 views | 01:06:47
4,584,783 views | 01:39:21
737,333 views | 01:06:44
105,240 views | 01:07:13
113,471 views | 01:33:49
7,874,022 views | 1:32:48
955,836 views | 01:02:40
55,974 views | 00:59:50
107,878 views | 01:03:48
59,005 views | 00:59:31
553,897 views | 01:17:01
142,317 views | 00:57:13
59,251 views | 01:34:35
473,194 views | 01:33:30
530,538 views | 01:24:26
212,066 views | 01:38:53
1,229,579 views | 01:27:13
1,401,650 views | 01:25:32
480,483 views | 01:39:51
525,545 views | 01:23:44
162,377 views | 01:02:32
192,035 views | 01:19:33
140,903 views | 01:21:33
815,433 views | 01:22:23
1,195,923 views | 01:22:11
462,514 views | 01:23:39
7,397,073 views | 01:33:30
302,637 views | 01:23:57
3,782,324 views | 01:38:44
1,643,306 views | 01:23:57
977,019 views | 01:27:52
766,417 views | 01:28:48
52,078 views | 01:24:33
783,128 views | 01:26:02
3,451,936 views | 01:22:35
452,244 views | 01:30:42
159,307 views | 01:31:59
108,595 views | 01:24:28
374,887 views | 01:35:31
538,726 views | 01:30:32
696,246 views | 01:28:02
1,161,734 views | 01:44:14
823,866 views | 01:16:48
3,002,767 views | 01:30:10
1,658,666 views | 01:33:00
95,178 views | 01:41:19
372,023 views | 01:35:29
273,624 views | 01:25:28
1,036,783 views | 01:25:19
2,430,756 views | 01:43:58
864,493 views | 01:36:21
334,369 views | 01:46:12
243,925 views | 01:02:50
167,609 views | 01:17:21
4,856,636 views | 01:30:56
281,865 views | 01:25:57
51,081 views | 01:01:50
144,912 views | 01:02:03
315,582 views | 00:48:49
293,925 views | 01:26:50
729,125 views | 02:03:40
231,658 views | 01:51:22
1,405,538 views | 02:08:02
1,380,721 views | 02:53:44
131,458 views | 01:54:16
89,722 views | 02:06:58
86,600 views | 02:19:44
230,548 views | 02:10:10
225,105 views | 03:01:37
269,862 views | 02:33:02
1,124,212 views | 03:05:19
192,434 views | 01:45:24