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This video explains how the urban is characterised by non-linearity.
To understand the difference between a linear world and non-linearity, let me introduce to you two of my heroes. They are no planners. They are mathematicians. One is Fibonacci, who lived ages ago. He brought us the wonderful Arabic system of numbers, which we are still using today. The other hero is Mandelbrot. He passed away just recently in 2010. These two are extremely interesting, as they explain to us non-linearity in an elegant way. In this lecture, I will first look at the nonlinear past, to go from there to the linearity of today. The Fibonacci sequence is an example of non-linearity. In the very past, the Fibonacci sequence and the proportions that came with it were considered as divine.
As if the gods were hidden in these structures, as if the gods were trying to tell us something by these wonderful algorithms. The question is, how do these defined proportions relate to urban design. I have to take it to France to answer this question in a quite elegant way. Join me to Ville de Richelieu. Ville de Richelieu is a product created by Cardinal de Richelieu in 1636. We all know Cardinal de Richelieu as the villain hunting the Three Musketeers in various adventure movies. In reality, it seems, he did a good job. As prime minister under King Louis the 13th, he was given by the King the opportunity to build a town, chateau, and park.
Now the question is how did he structure space to allocate his town, chateau, and park. He made use of the Fibonacci sequence, a divine and as well a nonlinear pattern. It’s all still very much there. Now, we’re going to make a jump to today, a time in which linearity and functionality prevail. Here too, we have an example to show how to see functionality and linearity, the garden city, proposed by Ebenezer Howard. The garden city concept is from the early 20th century. It is an absolute milestone in spatial planning. Despite its romantic touch, the concept marks the beginning of a functional era. Howard proposed a spatial separation of functions.
Units of production are to be allocated in the urban center, while consumption and pleasant life are meant to take place in the satellites, the garden cities. Satellites and the center are proposed to be well connected by direct lines of infrastructure. These lines are expressions of functionality. Well, there you are, all the ingredients of the modern city of the 20th century are there in Howard’s garden city model. In the highly planned environment, urban functions are separated from each other, while being well connected. It’s functional, predictable, and controllable. In such a world we consider to be linear. The linear world is the world we inherited. Our generation does not know anything else.
All is meant to be functional, straightforward, and clear, no room for multiple interpretation. We have great examples of this straightforwardness. For example, the Seagram building in New York, by Ludwig Mies van der Rohe. It relates to the Bower style, which is minimal, equal, and functional. Or [INAUDIBLE] Rietveld’s chair, it’s very much a chair, but not meant to sit in, as it will hurt your back. But it is a chair, indisputable. These are great examples of what we are, functional.
We see this everywhere around, these repetitive patterns of functionality. Look at all the apartment blocks in cities. Most would consider them boring. But that’s what happens when you want blocks to be functional. These will be straightforward and predictable. We can immediately see what they are, very much linear. The same counts for mono-functional neighborhoods, with patterns which are repetitive and predictable. And if one house gets outdated, the whole neighborhood will have to be upgraded. Because all the houses are the same. This is not much different from our forests. You might know we don’t have indigenous forests anymore. We’ve planted them, tree by tree, all are the same kind, positioned in straight lines. And if one gets sick, they all get sick.
Framing a world linearly and functionally has its limitations. If we open our eyes and we look around us, not everything we see does match very well with this linearity, with this functionality, with this predictability. Look at how we are using the bike, for example. It’s anarchy. Bikes are everywhere, quite often ignoring traffic regulations. And while the urban is perhaps very neatly arranged and very well structured, it can be heavily polluted too. The Netherlands is one of the polluted areas in Europe. Planners could not avoid this to happen through good planning. What about a crash of an airplane? These things do happen too, and they show us an uncertain world. We cannot run away from these uncertainties. They are happening.
They are very real. What will happen if we are willing to see the urban as a highly dynamic, surprising, and uncertain place, with its ups and downs? The urban being fragile, sometimes uncontrollable, full of unpredictable, nonlinear processes.
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Decision Making in a Complex and Uncertain World

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