Bin
Jiang
Faculty
of Engineering and Sustainable Development, Division of GIScience
University
of Gävle, SE-801 76 Gävle, Sweden
Email:
bin.jiang@hig.se
“All of
my life I’ve spent trying to learn how to produce living structure in the
world. That means towns, streets, buildings, rooms, gardens, places which are
themselves living or alive… depending on who you talk to, they’d say, ‘Well,
this stuff Alexander’s been discovering is a lot of nonsense. There is no such
thing as objectivity about life or quality.’ ... They are simply mistaken.”
Christopher
Alexander (1999)
Abstract:
Living
structure is a physical phenomenon and mathematical concept, through which the
quality of buildings or artifacts can be judged objectively. Living structure
is to beauty what temperature is to warmness. Just like a tree, a living
structure has two distinguishing properties: “far more small things than large
ones” (so called scaling law) across all scales from the smallest to the
largest, and “more or less similar things” (so called Tobler’s law) on each
scale. Living structure can be only generated in some step by step fashion by
two design principles (differentiation and adaptation) through the 15
structural properties.
Keywords: Living structure, third
view of space, wholeness, life, beauty
1. Introduction
If
the life’s work of Alexander (2002–2005) – The Nature of Order– had to
be summarized in one word, “beauty”, “life” and “wholeness” would be the three
top candidates. If allowed two words, it would be “living structure”. What do these
terms really refer to? Instead of getting into their detailed meanings, let us use
an analogue to clarify them first. If wholeness were compared to temperature,
then beauty or life would be like the feeling of warmness or coldness. The
higher the temperature, the warmer one feels, and the lower the temperature,
the colder one feels. The higher the wholeness, the more beautiful or the more life
one feels; the lower the wholeness, the less beautiful or the less life one feels.
Therefore, a thing or structure that exhibits a high degree of wholeness is
called a living structure. Opposite to living structure is non-living (or dead)
structure.
To
know whether a thing or space exhibits living structure, one can simply examine
whether it possesses “far more smalls than larges” across all scales ranging
from the smallest to the largest. For example, at the multiple levels of scale
or in a recursive manner – an entire tree, its branches, and its leaves (in
terms of the detailed texture) – there are always “far more smalls than larges”.
Therefore, a tree is beautiful or alive structurally, regardless of whether it
is alive biologically.
A
simple shape that lacks of detailed smaller structures is neither beautiful nor
alive. This is for the same reason why sans-serif fonts are less beautiful or less
alive than serif ones. For example, the font “I” (when shown as a sans-serif)
is not a living structure (one vertical line only) without “far more smalls
than larges”, whereas the font “I” (when shown as a serif) is a relatively
living structure (one vertical line and two little bars) with “far more smalls
than larges”. The difference between the non-living and living fonts may be hardly
sensed when the two fonts are too small, in particular when the letter’s
meaning is focused on. As a matter of fact, serif fonts in general are
objectively more beautiful than sans-serif ones.
This
article is intended to make it clear why living structure is beauty’s
temperature. More specifically, the
essence of beauty is structural or objective, lying in the notion of “far more
smalls than larges”, which accounts for a majority of our sense of feeling on
beauty. There is a clear sign that beauty is beginning to be accepted as an
objective concept in the literature of philosophy (Scruton 2009). Beauty is not just in the eye of the beholder
as once held, but exists in living structure. The phenomenon of living
structure is universal and pervasive, not only in nature but also in what we
made and built across all cultures, ethics, and religions, involving ancient buildings
and cities, as well as ancient carpets and other artifacts.
2. Living structure by
two examples
Alexander
first described the idea of living structures in a corner of an English country
garden, where a peach tree grew against a wall:
“The
wall runs east to west; the peach tree grows flat against the southern side.
The sun shines on the tree and, as it warms the bricks behind the tree, the
warm bricks themselves warm the peaches on the tree. It has a slightly dozy
quality. The tree, carefully tied to grow flat against the wall; warming the
bricks; the peaches growing in the sun; the wild grass growing around the roots
of the tree, in the angle where the earth and roots and wall all meet.” (Alexander 1979)
In
this living structure of the garden corner, there are many interconnected living
centers, such as the wall, the peach tree, the sun, the bricks, the wild grass,
the roots of the tree, and even the garden. This is a very good example of Alexander’s
miniscule observations on nature and on our surroundings.
Considering
another example of embryogenesis, a growing mouse foot is a living structure that
comes from continuous differentiation and adaptation (Figure 1, Alexander 2005).
In the course of the step-by-step development of the five days, many of the 15 structural
properties (Table 1) can be observed, such as strong centers, thick boundaries,
gradients, levels of scale, contrast, local symmetries, and finally, good shape
of the whole.
3.
Living versus less-living structure
A
simple comparison can help to prove that the modernist architecture and design usually
fail to create living structure, whereas traditional buildings and designs are
usually living structures. Two building façades and all their identified
centers are shown as individual polygons (Figure 2). The cathedral façade
contains over 500 centers, whereas the modernist one contains only a bit over
50 centers. From these two numbers, we can judge that the left is more living
than the right. Secondly, the cathedral façade has six hierarchical levels
indicated by the six colors, whereas the modernist façade has only two levels
represented by blue and red. In addition, all of the blue pieces on the
modernist building façade are exactly the same size, so look boring without any
variation. There is little doubt that the left is more beautiful or living than
the right.
Let’s
further look at the two logos of University College London (UCL) (Figure 3). The
new logo (http://tiny.cc/jpgxaz) was adopted in 2005, but
it is far less-living than the old one (http://tiny.cc/81gxaz). The old logo has at
least 19 centers, which hold five hierarchical levels (Figure 3a and 3b),
whereas the new logo has a maximum of six centers, which can be put at only two
hierarchical levels: the five centers as the figure, and the one center as the
ground (Figure 3c and 3d). In fact, two of the six centers are a bit too small
to recognize when the logo is small enough. It is clear that the old logo is
more living or more beautiful than the new one. Even by assessing the three
letters U, C, L, we can conclude that the old one is more beautiful or more living
than the new one, based on the fact that serif letters in general have more
centers – thus more beautiful – than sans-serif ones. To this point, the more-living
and less-living logos can really be said to a fact rather than an opinion.
The
two examples above demonstrate that living structure meets both the scaling law
(Jiang 2015) and Tobler’s law (Tobler 1970), whereas dead structure violates
these two laws. For example, the two bad designs – the modernist façade and
logo – are considered to be dead structures, for they have only two
hierarchical levels (indicated by red and blue). It should be noted that these
two bad designs are, by far, not the worst. All those buildings labeled by such
names as modernism, postmodernism, and deconstructionism belong to so-called dead
structures or disorganized complexity (Jacobs 1961). In this connection. we
found no better paper than the one by Salingaros (2014) that illustrates
vividly complexity in architecture and design; essentially, living structure is
organized complexity, while dead structure is disorganized complexity. Dead
structure or disorganized complexity violates scaling law across scales or Tobler’s
law on each scale, and is not created by differentiation and adaptation through
the 15 structural properties.
4. Summary
Living structure as a physical phenomenon
and mathematical concept help people to understand objective or structural
nature of beauty. It is a mathematical structure of physical space, which is
able to reflect in our minds psychologically: the more living the structure is,
the more beautiful one feels. Beauty and ugliness can be clearly defined by
scaling law; that is, a structure with a flat hierarchy – with maximum two
levels of scale only – is objectively considered to be ugly, whereas a
structure with a steep hierarchy – with at least three levels of scale – is
objectively considered to be beautiful. By claiming objective or structural
beauty, our intention is not to deny idiosyncratic aspects of beauty, which account
for only a small proportion of our feeling. This dominance of the objective
over the subjective can be compared to any statistical regularity with a
majority of agreement, such as an r square value of 0.75 instead of 1.0. In
addition to the hierarchy or scaling law, Tobler’s law plays an important role
in the objective or structural beauty as well. As one of the two laws of living
structure, Tobler’s law – or the notion of “more or less similar” – recurs on
each level of scale. The true meaning of “more or less similar” is neither “completely
same” nor “completely unique”, but something between the same and the unique.
These two complementary laws work together, governing living structures, with the
scaling law being primary, and Tobler’s law being secondary.
Acknowledgement
This paper is a shortened version
of the open-access paper (Jiang 2019), originally published by the journal
Urban Science (MDPI: https://www.mdpi.com/). This research was
funded by the Swedish Research Council FORMAS through the ALEXANDER project
with grant number FR-2017/0009.
References:
Alexander C. (1979), The Timeless Way of Building, Oxford University Press: New York.
Alexander C. (1999), The origins of pattern theory:
The future of the theory, and the generation of a living world, IEEE
Software, 16(5), 71–82.
Alexander C. (2002–2005), The Nature of Order: An essay on the art of building and the nature of
the universe, Center for Environmentaln Structure: Berkeley, CA.
Jacobs J. (1961), The Death and Life of Great
American Cities, Vintage Books: New York.
Jiang B. (2015), Geospatial analysis requires a
different way of thinking: The problem of spatial heterogeneity, GeoJournal, 80(1), 1–13.
Jiang B. (2019), Living structure down to earth and up
to heaven: Christopher Alexander, Urban Science, 3(3), 96,
https://www.mdpi.com/2413-8851/3/3/96
Salingaros N. A. (2014), Complexity in architecture
and design, Oz Journal, 36, 18–25.
Scruton R. (2009), Beauty: A very short
introduction, Oxford University: New York.
Tobler W. (1970), A computer movie simulating urban
growth in the Detroit region, Economic
geography, 46(2), 234–240.
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