We have come to the point in this course when we need to present the geometric properties responsible for the deep connectivity that I have discussed in previous chapters.Christopher Alexander has derived a set of 15 properties that all structures that we perceive to have “life” possess (Alexander, 2001).
Note that it is only after separating what has qualities of “life” from what does not that we have a body of examples from which to extract the sought-for geometric rules. Those rules are discovered by observation from these objects, as was achieved by Alexander. Once written down, we can then verify that all objects with the quality of life satisfy these rules.
The 15 fundamental properties uncovered by Alexander are the important beginnings of a massive ongoing investigation into the properties of matter. The 15 properties are phenomenological, yet we know from experiments that the phenomenon of life is based upon our biology and the physical properties of matter itself.
Therefore, starting from these 15 properties opens up a research program to discover why these geometrical rules are so important, and to explain them. It also drives us to seek further complementary factors that refine and improve our understanding of the phenomenon of life. Alexander himself has done this in Volumes 2 to 4 of The Nature of Order, and I have also been responsible for results in this topic. [Note: only the results ofThe Nature of Order Volume 1 are discussed in the current book.] Here is a list of the fifteen properties:
1. Levels of scale
2. Strong centers
3. Thick boundaries
4. Alternating repetition
5. Positive space
6. Good shape
7. Local symmetries
8. Deep interlock and ambiguity
13. The void
14. Simplicity and inner calm
I am going to use some notes on the fifteen properties from Lecture 6 of my book Algorithmic Sustainable Design (2010). The Leitner diagrams illustrating the properties are given there, and are now included in his own book (Leitner, 2015). A brief description of each property follows:
1. Levels of scale exist along with a scaling hierarchy. Repeating components of the same size and similar shape define one scale. Levels of scale have to be spaced closely enough in size (magnification) for coherence, but not too close to blur the distinction between nearby scales. Thus, a jump in scale by a factor of 15 is disorienting, whereas a factor of 1.5 is too close to distinguish one scale from another. A mathematical rule generates a distribution of scales via the logarithmic constant e ≈ 2.7 and the Fibonacci sequence: see “Applications of the Golden Mean to Architecture” (Salingaros, 2012). The whole point of adaptive design is to satisfy needs on the human scales, which range from 2 m down to less than 1 mm. The rule only says that you must accommodate all these scales.
2. Strong centers are formed when a substantial region of space is tied together coherently. It is useful to distinguish two types of centers—“defined”, and “implied”—that overlap and interact. A “defined” center has something in the middle to focus attention. An “implied” center has a boundary that focuses attention on its empty interior. Visual focus is a precondition for the use of spaces. Each center combines surrounding centers and boundaries to focus on some region. Centers support each other on every scale: this is a recursive hierarchical property.
3. Thick boundaries. A thick boundary is an “implied” center. According to the scaling hierarchy, a thick boundary arises as the next scale smaller than what is being bound. For this reason, thin boundaries are ineffective, because they skip over one or more terms in the scaling hierarchy, so the boundary is not connected by scaling to what it bounds. An “implied” center is defined only through its own thick boundary. Therefore, thick boundaries play a focusing role as well as a bounding role.
4. Alternating repetition helps in the informational definition of repeating components. Simplistic repetition is collapsible information, because what repeats is trivially coded (for example, take an empty or plain module X and repeat it 100 times): see “Why Monotonous Repetition is Unsatisfying” (Salingaros, 2011). Contrast, acting together with repetition, reinforces each component through alternation. This alternation helps to better define essential translational symmetry.
5. Positive space refers to Gestalt psychology, and links geometry with the basis of human perception. Convexity plays a major role in defining an object or a space, whether this is an area or a volume. We feel comfortable or uncomfortable in the spaces we inhabit for a combination of mathematical and psychological reasons. We strongly feel a threat from objects sticking out. We need to apply the positive space concept to both figure and background. Not only the building’s interior space but also urban space must be positive: see “Urban space and its information field” (Salingaros, 1999).
6. Good shape arises when symmetries reduce the information overload. Perceivable objects produce a represented shape from many separate 2-D views, which the brain can computationally manipulate in 3-D. “Good” means “easily graspable”, satisfying the brain’s innate need to compact information. Shapes that are not easily represented strain mental computation, hence they induce anxiety.
7. Local symmetries are symmetries within the scaling hierarchy. Symmetries must act on every distinct scale. “Symmetry” does not mean overall symmetry on the largest scale, as is usually understood. In organized complex structures, we have multiple subsymmetries acting within larger symmetries. All the symmetries should be nested hierarchically.
8. Deep interlock and ambiguity are other strong ways of connecting. Forms interpenetrate to link together. An analogy comes from fractals, where crinkled lines tend to fill portions of space, and surfaces grow with accretions. Two regions can interpenetrate at a semi-permeable interface, which enables a transition from one region to another. There is ambiguity as to which side of the interface one belongs while inside the transition region, and this is a good feature. Abrupt transitions such as a clean straight line, however, do not bind objects coming up to each other.
9. Contrast is necessary to establish distinct subunits and to distinguish between adjoining units. Contrast is also needed to provide figure-ground symmetry of opposites. Strongly contrasted regions can also be strongly connected. For example, the space under an arcade contrasts with open street space. False transparency reduces contrast, and reduced contrast weakens the design. An example of weak (ineffective) contrast is inside versus outside space separated by a glass curtain wall.
10. Gradients represent controlled transitions. They provide a method of getting away from uniformity, because that is a non-adaptive state. Subdivision also does this, however sometimes we should not divide a form into discrete pieces, but instead need to change it gradually. Examples include the urban transect: city transitioning to countryside, and in interior spaces: public transitioning to private realms.
11. Roughness. A fractal structure goes all the way down in scales—nothing is smooth: see “Scaling and Fractals” (Mehaffy & Salingaros, 2012). Ornament can be interpreted as controlled “roughness” in a smooth geometry. The relaxation of strict geometry to allow imperfections makes it more tolerant. So-called “imperfections” differentiate repeated units to make them similar but not identical—for example, hand-painted tiles. There is deliberate roughness in repetition that avoids monotony. Approximate symmetry breaking prevents informational collapse. Adaptation to local conditions creates roughness, since it breaks regularity and perfect symmetry.
12. Echoes. There are two types of echoes in design. First, translational symmetry: similar forms found on the same scale but at a distance. Second, scaling symmetry: similar forms existing magnified at different scales. Mathematical fractals are exactly self-similar. But all natural fractals obey only approximate, or statistical self-similarity—not exactly the same when magnified, but only “echoes”.
13. The void can be identified with plain structure at the largest scale of a fractal. The largest open component of a fractal survives as the void. It is not possible to fill in all of a fractal with detail. In “implied” centers, a complex boundary focuses on the open middle—the void. Therefore, an empty portion in necessary to balance regions of intense detail.
14. Simplicity and inner calm. This is a more subtle quality. Balance is achieved by an overall coherence and lack of clutter. Symmetries are all cooperating to support each other, with nothing extraneous or distracting. Coherent design appears effortless (but is in fact very difficult to achieve). We see this simplicity in nature, though it is never actually “simple” in the sense of being minimalist. “Simple” in nature means extremely complex but highly coherent. A system appears “simple” to us because it is so perfect.
15. Not-separateness comes after achieving coherence. Coherence is an emergent property—not present in the individual components. In a larger coherent whole, no piece can be taken away. Decomposition is neither obvious, nor possible. When every component is cooperating to give a coherent whole, nothing looks separate, and nothing draws attention to itself. This is the goal of adaptive design: a seamless blending of an enormous number of complex components. This is the opposite of willful separateness. Not-separateness goes beyond internal coherence, because the whole connects as much as possible to its environment.
The fifteen properties give rise to coherent form, which is so natural that it is hardly noticed—like nature herself! But we do perceive this coherence subconsciously, and it affects us deeply. Coherence is healing. We also immediately notice incoherence, in which the fifteen properties are absent. It disturbs, alarms, and excites us at the same time. This type of excitement is unhealthy in the long term. Architects and students most often wish to draw attention to their designs, and accomplish this by violating the fifteen properties. Doing so causes physiological anxiety for the users.
Whether consciously or unconsciously, architectural design since the beginning of the 20th century has cultivated the absence of the 15 properties. As a result, students and architects respond emotionally (very negatively) to them, reacting from their image-based conditioning. One cannot hide behind the excuse that what I’m talking about is only very recent knowledge, because architects have always been aware in some way of the fifteen properties. Form languages that we use widely today were developed to contrast with traditional form languages, and thus to deliberately break the 15 properties: see “Why Primitive Form Languages Spread” (Salingaros, 2006).
Since architects have avoided the 15 properties for one century, why apply them today to design the built environment? The reason is that we are still part of nature: human biology has not changed in one century. Yet during that time, we have been desensitized to go against nature and our reactions to natural and unnatural forms, denying our own biological makeup. Everybody agrees that our society is stressed, and that it would improve our health to go back to building structures and environments that help us to heal. This type of architecture can make a significant contribution to raising the quality of life.
It is true that part of the motivation for abandoning design according to the 15 properties was for practical reasons: a more rapid design process, standardization, manufacturing efficiency, strictly generic spaces to allow maximum flexibility of use, a “sleek, modern look”, etc. But now it’s time to recover what we have lost. It’s time to become reconnected with nature directly, as well as through the geometrical properties of what we build. With present-day technological sophistication, it is just as easy to implement architectural solutions that exemplify the 15 properties, as it is to continue to disregard the problem.
The question of styles needs some clarification. People grow tired of a style, then adopt another different one. But what we observe since the introduction of modernist architecture is a cycling through a related group of styles, all of which violate the 15 properties. Form languages did indeed change during the last several decades, but what they have in common is that they avoid the 15 properties. Innovative form languages have not come back to adopting the 15 properties, but remain in a geometrical domain of violation. This cannot be accidental—there is a meta-selection rule that keeps architects from using the 15 properties for design, considered as somehow “improper”. But we wish to focus on and implement what’s best for people, not to continue a biased stylistic dictate.