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For centuries, artists, philosophers and mathematicians have noted the special properties of the so-called “golden rectangle,” where if you take away a square, another golden rectangle remains, on and on infinitely. The human eye is drawn to those proportions, and they are evident everywhere from the facade of the Parthenon to a modern credit card. Yet an explanation of exactly why this pattern is so pleasing to us has been elusive. We talk with one professor who explains it with physics and explore the science of good design.
- Lance Hosey Chief Sustainability Officer, RTKL; author,"The Shape of Green: Aesthetics, Ecology and Design."
- Adrian Bejan J.A. Jones Distinguished Professor of Mechanical Engineering, Duke University. Author, “Design in Nature: How the Constructal Law Governs Evolution in Biology, Physics, Technology and Social Organization.”
Golden Rectangle Examples
The golden ratio appears again and again in art, architecture, nature and everyday objects. Modern television sets, index cards, Notre Dame Cathedral, the Taj Mahal and Salvador Dali’s “The Sacrament of the Last Supper” are all examples. See some of the most common — and most beloved — forms of the so-called “magic proportion.”
MR. KOJO NNAMDIFor millennia, artists, philosophers and mathematicians have known about the unique properties of the golden rectangle. Take a square away from a golden rectangle and what remains is another golden rectangle and on and on in an infinite spiral. These magical proportions can be found in some of the most famous designs in history, Da Vinci's "Last Supper," the facade of the Parthenon, but also in everyday objects all around us.
MR. KOJO NNAMDICredit cards, TV screens and paperback books, all share this golden ratio. Why does that shape have such appeal? At last, science has an answer, and it turns out science might hold the key to some other design mysteries. Joining us to discuss this is Lance Hosey, chief sustainability officer with RTKL. That's a global design firm. He's also author of the book "The Shape of Green: Aesthetics, Ecology and Design." Lance Hosey, thank you for joining us.
MR. LANCE HOSEYThank you.
NNAMDIAnd joining us from studios at Duke University is Adrian Bejan. He is the J.A. Jones Professor of Mechanical Engineering at Duke. He's the author of the book "Design in Nature: How the Constructal Law Governs Evolution in Biology, Physics, Technology and Social Organization." Adrian Bejan, thank you for joining us.
PROF. ADRIAN BEJANThank you for inviting me.
NNAMDIYou can join this conversation by calling 800-433-8850. You can send us email to email@example.com. You can send us a tweet, @kojoshow. Have you heard of the golden rectangle or the golden ratio? 800-433-8850. Lance Hosey, ancient Greeks believed that the golden rectangle also known as the golden ratio was the shape most pleasing to the human eye. Where do we see the golden rectangle in art and design?
HOSEYWell, you mentioned one example of the facade of the Parthenon, which is perhaps the most famous building in history, and it's based on the mathematical principles of the golden ratio which expressed as a rectangle is the golden rectangle. And so we've known about this for 2,000 years or more. You also see it in some of the most famous designs in history, the facade of the cathedral of Notre Dame in Paris.
HOSEYThe body of the Stradivarius violin is -- conforms to the same proportions, and in fact, many believe that's what accounts for the particularly beautiful resonant sound of the Stradivarius. The original iPod has the same proportions. And some of the most common designs that we carry around with us, including common credit card proportions and as well as paragraphs of texts, as Adrian is likely to tell you in a minute, the sort of ideal paragraph proportions or the golden ratio. So you see this everywhere, but we haven't known till the last few years why it's so popular.
NNAMDIAdrian, you have written about what makes the golden rectangle work for us. You say it's the shape we scan with our eyes most easily. Can you explain that, please?
BEJANWell, this explanation came to me as a -- how should I say -- an accident. The more general version of the principle is that we all attempt to be attracted to things that make our life easier and faster moving and safer. And we do that with looking at the right, like, frequency, living a life of pattern. And, yes, it turns out that if we can look at something and grasp it the fastest in order to get going, to move to safety, if you will, then we go for that.
BEJANAnd the physics of scanning a page with our two eyes which are on the horizontal says that the fastest way to scan is if the image is shaped in a particular way. And that particular way is such that the horizontal dimension is about 50 percent longer than the vertical dimension.
NNAMDIGoing to the telephone early in this broadcast because Anthony in Silver Spring has something to say to or about you, Adrian. Anthony, you're on the air. Go ahead, please.
ANTHONYKojo, thank you. You've once again proven that you have a knack for identifying genius. Hello, Adrian. It's Anthony Perez, Christian (unintelligible). How are you first? And I'm sorry I haven't gotten back to you. I've been extremely busy. But let me just say this to the -- to your listeners, Kojo, if Adrian Bejan doesn't receive a Nobel Prize within, say, the next 10 to 15 years, I will personally go and protest in front of Stockholm and make a big fool of myself.
NNAMDIWhy is this, Anthony?
ANTHONYThe constructal law is not a theory. It's a law of physics. And not only is it just the law of physics, but, like all fundamental laws, it has applications that reach into the other disciplines and concepts. I have been working using Adrian Bejan's theories for five years now, applying them in economics in a similar way to one of his predecessors and one of his mentors, Ilia Prigogine's mathematics of fractals, influenced derivatives.
ANTHONYAdrian Bejan's mathematics and Adrian Bejan's philosophy and his deep thinking about the constructal law and nature will have a great effect on our economic environment. And for one thing, he's using it to expand -- using the methods to expand the base, reduces turbulence, Adrian. I believe we are locking in to a way of reducing some of the bubbles or making the bubbles less dangerous when they appear in the economy.
NNAMDIAnthony, I'm glad you called because you will help to pique the interest of our listeners. We'll go into more detail about Adrian's theory later in this broadcast. But I wanted to get you call in early. So thank you very much for calling. You, too, can call us at 800-433-8850. Adrian, Anthony wanted to know how you were doing. You'd better clear that up.
BEJANI'm doing fine and trying to hang around until 15 year later.
NNAMDIAnthony, once again, thank you very much for your call. You, too, can call us at 800-433-8850. Before we get more into the theory, Lance, why is good design important? After all, even something badly designed can often get the job done.
HOSEYGreat question. It's really the heart of my book, "The Shape of Green." And I think it also, for a wide audience, can clarify why Anthony is so excited about Adrian's work. In a nutshell, it's this, that we think of good design as an art. It's driven more by the subjective personal taste of the designer than it is by anything else. But a growing body of research, including Adrian's, shows that certain shapes, colors, patterns have virtually universal appeal.
HOSEYSome are calling it neuroesthetics. Others are calling in bioaesthetics. The thought is that because of our evolutionary history, we seek out these things in nature and the world around us. Now the reason it's important is because the more that designers learned about this growing research, the more able they will be to create things with wide-lasting appeal.
HOSEYTherefore, the environment around us which, for most of us, is mostly constructed, it's designed, it's not natural per se, becomes more responsive to basic human needs. And therefore, it's something we're less likely to abuse. So there's an environmental component to it, but also more lasting appeal and, therefore, it helps us feel better in the environment around us.
NNAMDII was about to say things like paint color or having a window in our workplace can actually affect, it would appear, our physical well-being, right?
HOSEYYes. There are some patterns. There's a physicist named Richard Taylor in Seattle who's done a lot of work around natural fractals. Image a tree. If you look at it from a distance and look at it up close, it has similar shapes. That is called a fractal. And Richard has shown that certain patterns of fractal can actually reduce stress. So using skin conductance tests, for instance, he's shown that it can reduce stress in people just by glancing at these images by as much as 60 percent.
HOSEYSo the well-being possibilities for enhancing our kind of comfort and well being, the medical properties of this are astounding. But also, as Richard says, because in the U.S. alone, we spend about 300 billion a year on stress-related illness, the potential for a design to have an economic savings is enormous.
NNAMDIAdrian, scientists for a long time have believed evolution dictates the patterns in nature and that they were essentially random. But you find one central tendency in everything that moves. Tell us about flow system.
BEJANWell, everything that is alive, biological or rivers out there is moving, and at the same time, it is morphing freely. It is changing overtime to flow more and more easily. This holds for the river basin which is a dynamic, not static. It also holds for in our discussion here, the evolution of our species which is really a hand and glove of humans with artifacts and add-ons and technology and machines around them.
BEJANAnd it is all -- this movement or this evolution of the design is toward moving more and more easily, moving farther with a longer lifespan. That is the phenomenon of the design and nature, and that is what's covered by the constructal law. The constructal law is a very short statement summarizing what I just said, summarizing this tendency. And...
NNAMDIIt is another law in physics that governs everything around us in much the same way that gravity does, correct?
BEJANLike, yes, but also very much in the same sense as the first law of thermodynamics which is the conservation of energy or the second law of thermodynamics which is the idea of irreversibility or that everything that flows from high to low. This is the, you know, like heat from hot to cold. The constructal law is about changing the design in this evolutionary movie, if you want, from a drawing that flows to one that flows more easily.
BEJANAnd this here that I would like to add to Lance's comment and your question about the design, design is basically a drawing or an image, and it has, of course, pleasing qualities that accounts for the, let's say, golden ratio phenomenon that we're attracted to the image. But design also has performance. And today's design is really destined to be replaced by a better one tomorrow if it is free to be changed. And that is what why we consider as bad is, in fact, a candidate for improvement or replacement in the immediate future.
BEJANAnd so we keep in mind the performance because it is the performance that evolves toward, well, being more and more economical. In time, this -- from this comes everybody's economic sense, everybody's long list of things that he or she likes, and -- for example, health, safety, including the previous segment on the show where the speaker spoke of this structure being an expression of our, you know, urge to find a design to make it easier to get around. Well, that -- we're going to have...
NNAMDISpeaking of designs that make it easier to get around, you used the Atlanta Airport as an example of a flow system. Much as people might complain about that airport as we do about all large airports, it actually functions very well. There's a main artery where the air train runs with a series of concourses perpendicular to that. Can you describe why and how that works as a flow system?
BEJANIt works just like the scanning of an image faster when the image is shaped as a credit card, seen from above at the Atlanta airport as a credit card. The scanning is done by all of us with our bodies, either in our shoes, meaning walking or sitting on our bottoms on the train. And the shape is such that all of us on that area move the fastest from a gate -- any gate to another place, and that is why the Atlanta airport is really the icon of where the design of any urban area comes from.
BEJANThe tiniest element in the city is tiny streets are kin to that train in Atlanta. And the walking, straight or wobbly across the lawn in front of the house, that is the equivalent of walking on the concourses. And speaking of Atlanta as an icon, out of nowhere, the best airports of the world, the newest -- the newest additions to the airports are actually speed walking in the direction of looking like the Atlanta Airport. That is the sign of natural design.
NNAMDILance, what do you find interesting as an architect about these theories?
HOSEYWell, the beauty of it is that if you look in nature, you see a lot of very similar shapes, patterns, images, lightning, the human lungs, a river delta, et cetera, trees. They all have these very similar patterns. And Adrian's theory beautifully shows the physical and mathematical properties that account for those similarities.
HOSEYAnd essentially in a nutshell, it -- those shapes aid the flow of energy, information and materials depending on the situation. So fractals -- for instance, I mentioned that same physicist, Richard Taylor, has shown that Jackson Pollock's late work conforms to this idealized density at a time when he was...
NNAMDIAnd he was not conscious of that.
HOSEYHe was not conscious of it. And I've joked that, you know, he spent decades finding this optimal pattern. Had he just known about this theory, he could've gotten to it more quickly and moved on to something else. But -- so the point is that the richness of these ideas, I think, eventually will completely transform designs so that if you think about sustainability and designs, so design that enhances or is more compatible with nature, one of the theories that we should behave more like nature. So we should learn more about nature's properties in order to make more responsive environments.
NNAMDIAdrian, you point out why it's less helpful to study the individual pieces of a successful design like the Atlanta Airport and copy those elements than it is to understand that principles at work behind that design. Can you explain?
BEJANWell, understanding at all levels is useful. The new aspect that construct the law elevates is that in addition to understanding the pieces where how the elements work, it is important to understand how the whole morphs so that the whole flows easier. This is an important direction which is new these days in science. It is a direction relative to reductionism. And the constructal law is really the law of physics that speaks of the behavior of the whole system to generate design and to improve it. So that's the new part that animates scientists these days around the law.
NNAMDILance, but while many designers, engineers, architects, in fact, use these principles, we discussed the layout, for instance, of the Atlanta Airport. Do you think that many of them recognize an underlying principle? Or is it trial and error?
HOSEYPersonally, I think it's mostly trial and error. As I mentioned before, designers and architects are trained to think about developing their own "voice." The most celebrated architects, the ones that the typical person on the street can name are famous, are well-known because they have developed a "signature style." And that has more to do with self-exploration, self-expression in the same way that we think of art than it has to do with creating buildings and places that respond better to people's needs, and as Adrian said, perform better.
HOSEYSo what kinds of structural principles would use as little material as possible to create a durable structure. There are architects in history who've explored that, Antonio Gaudi in Barcelona, the Sagrada Familia Cathedral, for instance, the columns there which are shaped like trees. He was years ahead of his time in understanding geometry and structure and the flow of gravity through material in order to use little material to perform that function.
NNAMDI800-433-8850 is the number. Why do you think we find certain shapes and patterns beautiful? Do you think science can explain it? 800-433-8850. I will start with Benedict in Manassas, Va. Benedict, you're on the air. Go ahead, please.
BENEDICTGood afternoon, everyone. Thank you for taking my call. Your guest is 100 percent correct. The ancient ones comprehended the dynamics of shapes to the point where they actually built civilizations. We can go back and use structures all over the planet reflecting this. When we look at the structures we have today, it would be interesting to see what someone would say 2,000 years from now.
BENEDICTWhat did we do? What did we learn? And Adrian is correct. The young man who called and praised him, he is absolutely correct. We should look at these things and explore the possibilities, not only in structure but in other areas to help build the civilization and make it better. Thank you.
NNAMDISo the use of this in economics and in other fields of science becomes particularly important. Care to comment, Adrian?
BEJANYes. Actually, this is a very good comment from the caller, but also the previous comment by Lance is right on the money. The Atlanta Airport and all the other structures you point out, including the ancient Greek structures come from art, from trial and error, if you will, from trying to obviously make it not only pleasant, but functional and high-performing.
BEJANThe principle, the law, this constructal law, a law of physics provides to us today is the knowledge of how to fast forward this process of doing the right thing along with some bad things, to -- how to fast forward and how to do things, but also what not to do on the way to a better life for everybody on the landscape. So that is where the constructal law comes in. Incidentally, that's where all the laws of physics come in. They are all useful in this regard. Science is there because it is useful.
NNAMDIGot to take a short break. If you have called, stay on the line. Benedict, thank you for your call. The number is 800-433-8850. You can send email to firstname.lastname@example.org. We're talking about good design and the scientific basis of it. 800-433-8850. I'm Kojo Nnamdi.
NNAMDIWelcome back to our conversation about design, what is pleasing to the eye and the scientific basis of it. We're talking with Adrian Bejan. He is the J.A. Jones professor of mechanical engineering at Duke University. He is the author of "Design in Nature: How the Constructal Law Governs Evolution in Biology, Physics, Technology and Social Organization." He joins us from studios at Duke.
NNAMDIJoining us in our Washington studio is Lance Hosey, chief sustainability officer with RTKL, a global design firm. He's the author of the book "The Shape of Green: Aesthetics, Ecology and Design." You can join our conversation by calling us at 800-433-8850. You can also send email to email@example.com. Here is Dan in Silver Spring, Md. Dan, your turn.
DANHi. Thanks for taking my call. Lance, it seems like your finding sort of a mechanistic view of aesthetics whereby, like, designing should be in form by all the scientific regenerated data which I happen to agree with the data itself. And so my question is, like, with architectural education going forward, how would you train an architect.
DANLike currently, I don't know if you would agree with me, but there's a preponderance of theory and technology and computers producing all the sort of fantastical designs. When I think about your findings and other people similar to you, it seems like we should put the human and their perception of space at the center. And I was wondering what you thought about that.
HOSEYSuch a great question. I mean, education really is the key. In order for designers to become more aware of possibilities, they need to become more informed about them. I wouldn't call it mechanistic so much as just better informed. But you're right, there are suddenly the last several years, decade, decade and a half at the most, there are emerging techniques and tools, computer programs that allow us to study these kinds of things in ways we'd never had before.
HOSEYMostly, they've been used to create forms that are either playing to the architect or designer's personal taste or forms that are more responsive to environmental conditions. To date, they haven't really been used as much to create things that draw from this research. The beauty of it is as Adrian said that evolution and the way that nature changed over many, many eons, if we think about new computer techniques as a way of speeding up that process and getting to more elegant and efficient solutions more quickly, we have that ability now, and we've never had that in the past.
NNAMDIWhen you talk about nature, you point out that even though we're following the evolution of nature, we talk about good design in terms of functionality. And there are some great designers like architect Frank Gehry who designed buildings that sometimes don't seem to be that functional. But you point out that nature isn't always efficient either. What do you mean by that?
HOSEYWell, nature is sometimes efficient in the sense that if you think about a honeycomb, a honeycomb is extremely efficient with material. That's why it has that shape, a hexagon being an extremely efficient shape. The quill of a bird feather, for instance, is very efficient with the material it uses. But there are other aspects of nature which if you look at it from that point view would seem fairly "wasteful."
HOSEYIt's been said that if you think about -- we're teetering in on cherry blossom season here in D.C., and all those cherry blossoms don't really need to happen the way they happen in terms of just efficiency of material. There are plants and animals that put a lot of energy into these fairly flamboyant images, and it's to attract other species.
HOSEYSo, again, it comes down to the law of attraction. The way -- one of the ways that life continues is by drawing other animals in, right? So something that appeals to the eye may not be efficient from a material conservation standpoint, but it's extremely efficient in attracting other things.
NNAMDIAdrian, you point out that what we're talking about today is really common wisdom. We talk about going with the flow, seeking the path of least resistance, taking the shortest route. So should it be any surprise that these universal tendencies are, in fact, undergirded by a natural law?
BEJANNo, but that is the way science happens. The wisdom is in everybody in all the generations. And after enough wisdom, after many generations, finally, the new one says, enough. Let's put a capstone on it and remember it with just one statement, and that statement is the law of physics. To the list of common wisdom that you read, I would add one that came to me as I was lecturing yesterday.
BEJANIt is the truth that the world is small or the world is getting smaller. We all seem to bump into the same people every hour or every day. And the reason for the latter is that actually the world is -- first of all, the world is not getting smaller, it can be measured. The fact is that we have move on the landscape through channels, through our own rivers and the rivulets, and those are few. And the people in those channels are like us, they are not many, and we bump into them.
BEJANThose of us who travel frequently, we see the same faces in the business lounges at airports. We don't know these people. They are not like us, but they are flowing along with us in those very few special channels. So our movement -- and now this goes back to Anthony Perez's point early on about economics -- is with design on the landscape that is in space and in time.
BEJANEconomic activity is river basin, on top of river basin, on top of river basin of -- you name it, transportation, transactions, freights, education and all these other things that spread, including information, which is really the flow of how to make changes in the designs. And these designs are actually invisible. But they become visible or they are illuminated by those who possess the principle.
NNAMDIOn to Ruby in Rockville, Md. Ruby, your turn.
RUBYI am so daunted to even be on the air right now. Thank you for taking my call. This is like an answer to a dream for me. So I'm a fine artist, and right now, I am working out a design problem. And I'm working on designing a Jewish marital contract for some clients, and I had spent a week of trial and error regarding trying to see if I can create a square of this format that might be as pleasing as the golden ratio.
RUBYAnd I was curious to know if this wonderful duo that you have had any tricks up their sleeves for me. And also I wanted to know if your book would be comprehensible to an artist who is in bad need of some math review. And could I understand what you are writing about if I were to pick up your book?
NNAMDIFirst you, Lance Hosey.
HOSEYYes. Well, I wrote the book myself, so I'd like to think that it's comprehensible. My friends tell me it is, so I'm going to say, yes, pick it up and -- but a good place to start might be, I think, The New York Times article that I did a few weeks ago, which is linked on...
NNAMDIIt is called "Why We Love Beautiful Things."
NNAMDIYou can find it online.
HOSEYIt's a really good recap. If you find that to be comprehensible, then you'll find the book comprehensible. So -- I won't try to solve your problem for you because it sounds a little daunting, how to make a square as pleasing as possible. However, I will say that I think graphic design is one of the richest fields in which to explore all of this because it's really all about image.
NNAMDIRuby, thank you very much for your call.
NNAMDIAnd good luck to you.
NNAMDIHere is Jen in Washington, D.C. Jen, you're on the air. Go ahead, please.
JENWell, you've moved on past my -- so far, I've had half a million thoughts. But specifically, I called to say -- and I think, as the conversation has progressed, they'd both agreed with me in as much as you were saying that Jackson Pollock's could have gone -- gotten through that idea and gone on to something else. I think that kind of would have been a shame if he did one and said, oh, I got it, and moved on.
JENBut specifically to say that artists and two-dimensional artists and performing artists have always pre-staged what has been later defined by mathematics and used as a rule, but to say that we can hasten the progress of Mother Nature or evolution by using computers, I think, leads us down a dangerous path. And we might want to see it as an aspect of the larger forces that play in evolution, and it's -- it seems hubristic to put the human control on driving evolution. And that maybe -- you might want to include...
NNAMDIWell, I'm not sure that what -- that's what they're saying. I know that Lance had said in the past that we often miss the importance of basic design, focusing instead on technology. And I'd like to hear what Adrian says in response to your comment, Jen. Adrian.
BEJANThe -- first of all, there's nothing dangerous in going with the flow. Had it been dangerous, I've fallen over the cliff a long time ago. That's the evidence. The evolution that the -- meaning human evolution that fits under the constructal law tent is the evolution of the human and machine species. There's -- there is us, of course, evolving none at all because that took millions of years, and the technology in which each of us is encapsulated. It is that that evolves, and it is for our good.
BEJANIf it is not good, it is discarded or forgotten. And everything is going in one direction in gulps or smoothly, but in any case, is not to be feared. Our -- you spoke of two-dimensional artists. There are plenty who have been going in the same direction in three dimensions. Science itself is about design. Most of us in science overlooked this history of ours. Science began with geometry, which is the science of figures, images, then continue with mechanics, which is the science of moving images, moving figures, connected figures.
BEJANThis is why the earlier caller referred to mechanistic. That is the old name, the first name of physics. And now the bigger name is physics, which means everything. Physics is one name for it. The other name from Latin is nature or natura, which means she who gives birth to everything. And in this birth, we belong. What the humans do is natural. Human and machine moving on a landscape are no different than the water of the Mississippi river basin. We're all moving mass from here to another place.
NNAMDILance Hosey, you wanted to comment?
HOSEYI would just going to clarify that I wasn't referring to speeding up evolution in nature. I was referring to speeding up evolution in design. I also think that design, particularly architecture, is very different from art in the traditional sense in that it's something that is in our everyday life. We spend 90 percent of our time indoors, in buildings, that is. So they have a different responsibility to become places that we connect with it, places that are responsive to our needs, much more so than, say, a painting that you visit in a gallery.
NNAMDIWe're running out of time very quickly, but if you can do this in 30 seconds or so, Adrian. We don't want to go too far into academic debates, but design in nature was until fairly recently a controversial concept for many scientists. Why was that?
BEJANBecause of the unfortunate happening that design in English has two meanings.
BEJANOne, which is the original one, is design means drawing. It comes from disensio in Italian. That is the meaning that I employ. The verb is the second meaning, to design, which carries with it the being, the entity, the designer, which, of course, is an entire -- entirely different subject of discussion. It's actually older than science. It is called religion. Over here, we're talking about the principle, well -- yeah, the principle of why we are attracted to certain designs...
NNAMDIWe got about 10 seconds.
BEJANYeah. We're attracted by the shape, by the beauty and by the performance.
NNAMDIAdrian Bejan is the J.A. Jones professor of mechanical engineering at Duke University, author of "Design in Nature: How the Constructal Law Governs Evolution in Biology, Physics, Technology and Social Organization." Lance Hosey is chief sustainability officer with RTKL, a global design firm. He's the author of the book "The Shape of Green: Aesthetics, Ecology and Design." If you'd like to hear more about the ins and outs of design, tune in to "Metro Connection" tomorrow at one.
NNAMDIYou'll hear about plans for new Chuck Brown memorial, a former slave who built a thriving dress design business for the fashionable women of Washington and the architectural feature that's nearly everywhere in D.C. and yet almost invisible. Thank you both for joining us, gentlemen, and thank you all for listening. I'm Kojo Nnamdi.
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