In this interview, Bin Jiang discusses how he discovered Christopher Alexander’s ideas, how these ideas foresaw Google PageRank before Google, how they are more profound than Benoit Mandelbrot’s fractals, about their connections to scientific discovery, and how his own pioneering mathematical work directly applies to projects at Building Beauty.
David Getzin: What are some of your ideas for the school? How did you come across Christopher Alexander’s ideas?
Bin Jiang: I came across The Nature of Order through reading Nikos Salingaros’ papers and books, so I ordered the four-volume book in my school library when it was first published. But I did not read it in detail until around 2008 after I have studied urban street networks for more than 10 years, and published many papers on street hierarchies, power laws, and traffic flow prediction, very much along the line of statistical physics.
To be honest, The Nature of Order is not an easy reading for me, particularly at the very beginning. However, as soon as I started to capture Alexander’s ideas – his profound thought in design, I could not stop, so I read all his previous works: about 16 books and many other papers and reports as much as I can get. From my experiance, his works should be read as a whole rather than fragmented pieces. As I remarked in one of my papers, Alexander’s living geometry is more profound than Benoit Mandelbrot’s fractal geometry; fractal geometry is mainly for understanding complexity, while living geometry for creating complex or living structures.
Now I can link my quantitative studies on cities to Alexander’s theory of centers or living geometry. For example, there are two fundamental laws of geography: Scaling law of far more small things than large ones, and Tobler’s law of more or less similar things, which is also referred to as the first law of geography formulated by Waldo Tobler in the 1970s: “everything is related to everything else, but near things are more related than distant things”. The scaling law can be more truly rephrased as the scaling hierarchy of numerous smallest, a very few largest, and some in between the smallest and the largest. In fact, scaling law is essentially about differentiation – one of the two design principles embedded in Alexander’s 15 geometric or transformation properties. The other design principle adaptation is in line with Tobler’s law. These two laws can be said to be those of living structure, which inheres in space across scales ranging from the Planck length (10^-43 m) to the scale of the universe itself (10^27 m). These design principles, or laws of living structures, can be directly applied to design of our built environment. These are also some of my ideas for the buildingbeauty school.
David Getzin: Could you summarize about your views on how Google PageRank and The Nature of Order connect?
Bin Jiang: This is a very deep question! We know PageRank is a key technology behind the phenomenal success of Google. In my paper entitled “Wholeness as a hierarchical graph to capture the nature of space”, I developed, based on Alexander’s definition of wholeness, a mathematical model of wholeness or life or beauty. In the model, I combined a topological representation of space and PageRank metric in order to measure or quantify degree of wholeness or life or beauty. The power of PageRank lies on its recursive definition: an important page is one to which many important pages point. As an example, to ask how important a person is, you must know how important the friends are, the friends of these friends, and the friends’ friends’ friends, and so on until virtually all people on the planet are considered. Alexander defined wholeness or life or beauty also in a recursive manner; see an Appendix in Book 1 of The Nature of Order – a beautiful center is one which many beautiful centers support. Here I would like to point out a fact that Alexander had the very first edition of The Nature Order in 1981, one year before his famous debate with Peter Eisenman at Harvard. Although Google’s PageRank idea was initially taken from the literature around the 1980s, Alexander independently developed this idea of mathematics, by which I mean that the recursive definition of wholeness or life or beauty is really original.
David Getzin: Does it sound right to you that because of PageRank deals with hyperlinks, architectural spaces that share proximity are related in terms of how they enhance each other or not? (This leads to discussion of Strong Centers.)
Bin Jiang: Yes, you are right! An architectural space – actually any space as noted by Alexander, is a complex network of numerous nesting and overlapping centers – the fundamental idea of the theory of centers or living geometry. This network thinking or precisely complex network has become very hot in the science community following the works of Duncan Watts, Albert-László Barabási, and Google’s two founders around 2000. BUT, Alexander had the complex network thinking in the 1980s, even earlier as shown in his classic – “A city is not a tree”. I had some remarks on Alexander’s pioneering thinking in these two papers:
Yes, there are far more low-degree centers than high-degree centers. This is what underlies scaling law or differentiation principle. Eventually, strong centers are emerged within a complex whole.
David Getzin: It certainly appears that this applies to the natural world just as much as to the world of architecture.
Bin Jiang: Yes indeed, Alexander’s work is beyond architecture, and brings science and art or humanities into one towards the third culture (with respect to C. P. Snow’s famous lecture on two cultures). I am a geographer, so I have tried to provide analytical evidence that geographic space is a living structure at country scale, at city scale, at building scale, even at the scale of an ornament. Living structure exists not only at the scale of geographic space, but all scales ranging from the smallest (Planck length mentioned above) to the largest (the scale of universe). To this point, I should mention the last year’s Nobel Prize to three quantum physicists for their key contribution on topology. I truly believe the topology is related to living structure at some finest scales.
David Getzin: Regarding the work with the school, it is useful to have both quantitative and qualitative methods at hand so you can measure with feeling as well as complimentary metrics. You can compare this to other advances in science, such as color. What are you most looking forward to in bringing this type of research to the school?
Bin Jiang: I truly believe that Alexander’s work is essentially quantitative, although he suggested using human feeling or the feeling of wholeness to measure degree of wholeness or life or beauty. Of course the quantitative would lead to the qualitative – living structure, or degree of life or beauty. Let’s use temperature as an example. Before the thermometer was invented, we human beings could sense temperature based on our feeling – the feeling of temperature, so we can sense something hot or cold. Now with thermometer, we can accurately measure temperature. This is the same for wholeness or life or beauty. With the mathematical model (or beautimeter) I mentioned above, we can measure degree of wholeness or life or beauty more accurately. I therefore look forward to applying beautimeter or the kind of research to the school in Naples.
David Getzin: So it seems that this type of feeling [of wholeness] becomes more like a distinct type of sense perception, like perceiving [other objectively measurable phenomena] color or harmony?
Bin Jiang: The feeling of wholeness is objective, so it is unlike idiosyncratic feelings, which vary from people to people. Alexander said that 90% of our feelings are shared, and idiosyncratic feelings account for only 10% of our feelings. I tend to put beauty into two types: surface beauty which is in the eye of the beholder (being subjective), and structural beauty which is objective. Taking human beings for example, we all have different or unique beauty on the surface. However, structurally or at a deep level, we are all the same in terms of the scaling hierarchy of numerous atoms (being the smallest), dozens of organs (being the largest), and some in between the smallest and the largest). It is the fine structure or scaling hierarchy that makes us to have spirit or soul, according to Alexander.
David Getzin: Are you looking forward to pursuing the use of these metrics with students in the building environment in Naples?
Bin Jiang: Absolutely! In order to build a good or beautiful environment, we must rely on the 90% of our shared feeling – the feeling of wholeness, rather than idiosyncratic feelings. Unfortunately, modern architecture and modernist urban planning have relied on the 10% idiosyncratic feelings for building our environment. Misguided by the arbitrary feelings, there is little wonder that the built environment has been deteriorating. According to Alexander, the value of built environment is NOT an opinion, but a matter of fact. It is time to rely on the scientific thinking or Alexander’s living geometry to make or re-make, to heal or re-heal our built environment.
Thank you very much David for the stimulating interview!