Systemics and complexity:
concepts and approaches for
PhD Program in Architecture, Built environment and Construction engineering
Politecnico di Milano
Milan, December 2015
Why are we interested in systems?
Entities are assumed to possess properties. Examples are
given by their weight, age, and geometrical properties.
Systems are entities that do not posses properties.
Systems acquire properties. A non-complex system
continuously acquires the same property.
Systems may acquire stable properties through functioning
such as devices. Examples are given by electronic circuits
converting into systems such as radios, computers,
amplifiers, and TV sets when powered, i.e., functioning.
Complex Systems continuously acquires variable multiple
coherent instantaneous sequences of different
properties such as for the so-called emergent systems.
Examples are given by flocks, swarms, anthills, road
traffic, industrial districts, cells, markets, lasers, and ...
... cities and their properties, e.g., morphology, energetic
behaviour, ecological behaviour, water management,
transportation system behaviour of the inhabitants; building
sites; and problems such as conservation, post-occupancy
evaluation, building performance evaluation, reuse, urban
models, evaluate ecological impacts, influence of
architecture on emergence of social systems and vice-
versa, resilience, etc.
What are Systems?
A system has been intended as an entity having properties
different from those of what are considered elements by
the designer (for artificial systems) or by the observer (for
A necessary and sufficient condition for the establishment
of systems is that elements, as designed (for artificial
systems) or represented (for natural systems) by the
observer, INTERACT in a suitable way.
We may assume, in short, that two or more elements
interact when one’s behaviour affects the other’s one as
observed by the observer.
Examples of such interactions are processes of mutual
exchange of energy (e.g., collisions and magnetic fields,
where vector fields exert a magnetic force on magnetic
dipoles or moving electric charges), matter (e.g.,
economic interchange) or information (e.g., prey-
Very briefly, in architecture interaction
is given by usage.
Sets Structured Sets Systems Subsystems
Floors of building
belonging to a
or grouped by age
Cells available for
Living beings Organs
Casual words Words in
A story, poem Chapters, verses
listed by the
structured by the
outline of an
electronic circuit in
when the board is
Group of components
classed by function
such as power
Animals per age
Groups of puppies,
Design systems or model a phenomenon
as a system
1. Systems are considered in an objectivist way when they are
artificially designed, i.e., we know the component parts and how
they interact because they were designed that way.
2. Systems are considered in a constructivist way (as for natural
systems which have not been artificially designed) when the
observer decides to apply a level of description (i.e., partitioning
and interactions) to those systems, as if they had been
designed as such. In this case, the observer constructivistically
models phenomena as systems, by assuming elements and
interactions. When this level of description works for
applications, it is often assumed to be the true one within the
conceptual framework of a discovery, thus resuming an
What are non-systems?
Depending on the level of description and on the model
adopted by the observer, an entity is not a system when its
properties are states, considered as not necessarily being
supported by a continuous process of interaction amongst
Non-systems are entities considered by the observer as
possessing non-systemic properties.
Only systems may acquire systemic properties, while
systems and non-systems may possess non-systemic
For instance, the property of a set of boids establishing a
flock is continuously established and this continuity is
considered as the coherence of the collective or coherent
behaviour of boids.
It should be stressed that systemic properties are not the
result of interactions.
Systems and their properties are established by the
continuous interaction among elements (e.g., an electronic
device acquiring a property when powered on, leading to
interactions amongst the component elements) and not as a
States are non-systemic properties, i.e. properties of non-
systems like a new colour obtained from mixing primary
colours (e.g., Red-Green-Blue), and of entities possessing
properties like weight, speed, the Avogadro number and
When elements of a system stop to interact than the system
degenerates into a set (the functioning stops).
A formal introduction
Ludwig von Bertalanffy (1901 – 1972), considered to
be the father of General System Theory, described a
system S as characterized by suitable macroscopic
interdependent variables Q1 , Q2 , . . . , Qn, whose
instantaneous values specify the evolutionary states of
/ dt = f1
, …, Qn
/ dt = f2
, …, Qn
/ dt = fn
, …, Qn
Emergence of Systems
In general, systems may be established or modelled as
such by considering
a) structure between elements (structure is a specification
of organisation. Organisation is a network of
relationships or interactions), and as
b) phenomenon of self-organisation and emergence (not
Systems are established by:
a) A structured functional way, when organisation is intended
as a network of pre-established functional relationships
which control the manners of interacting.
Rules of interaction are either determined by following a
design or constructivistically intended as such by the
In both cases they are sufficient conditions for establishing
Structured rules completely define the way in which
elements interact, i.e., they define all the degrees of
freedom possessed by interactions between elements at
the specified level of description.
Examples include mechanical devices, such as engines,
and electronic devices, such as circuits.
Examples of non-designed systems are natural entities
modelled as organised systems by the observer, such as
organs performing given functions in living beings and
b) Self-organisation processes considered as given by
continuous but stable, for instance, periodic, quasi-
periodic and predictable, variability in the acquisition of
new structures, as for Bènard rolls, structures formed in
the Belousov-Zhabotinsky reaction, swarms having
repetitive behaviour, lasers, ferromagnetic and
superconducting systems, and dissipative structures
such as whirlpools in the absence of any internal or
Stability of variability, e.g., periodicity and synchronicity,
corresponds to stability of the acquired properties.
c) Processes of Emergence considered as given by
continuous, irregular, unpredictable and coherent
sequences of processes of self-organisation, i.e., new
• flocking and swarming when having unpredictable
behaviour in presence of perturbations.
• communities of mobile phone networks, industrial
districts, markets, morphological properties of cities and
urban development, landscapes, networks like the
Internet, and queues.
There are different definitions of complex system.
•a system is complex when coherent processes of
emergence occur within it;
•a system may be considered as complex when its
evolutionary paths fall inside the basin of an attractor;
•a system may be considered as complex when its
evolutionary paths and properties are modeled by networks
and related properties.
They are multidimensional and coherent.
Coherence in non-complex systems coincides with the
acquisition and keeping of the same property.
Coherence in self-organised systems is given, for instance,
by the regularity, periodicity, and synchronicity of
sequences of structures.
Coherence in emergent systems is given by the keeping of
properties acquired by multiple, continuously changing
processes of self-organisations occurring within the same
system. For instance, shapes, collective intelligence and
This term is used to denote a corpus of systemic concepts, extension of
systemic principles by using, for instance, analogies and metaphors.
This expression is used to denote the general methodological aspects of
Systemics, considering, for instance, identification of components,
interactions and relationships (structure), levels of description, processes of
emergence and role of the observer.
General System(s) Theory
This expression has been introduced in the literature to refer to the
theoretical usage of systemic properties considered within different
disciplinary contexts (inter-disciplinarity) and per se in general (trans-
disciplinarity). Current research identifies it with the Theory of Emergence,
i.e. acquisitions of properties, although it relates to science of complexity.
This expression, often inappropriately used as shorthand for General
Systems Theory, relates to First-order cybernetics and Systems
Engineering for applications such as Control systems and Automata.
Approaches and models
1) DYnamic uSAge of Models (DYSAM)
The search for coherence
The concept of DYSAM applies when dealing with
complex systems, in which we cannot, in principle, resort to
a unique model (assumed as the correct one) to describe
the system being studied.
Thus we are forced to allow for a multiplicity of different
models (and modeling tools), all related to the same
The purpose is not to select the best one but to use all of
them together coherently). For instance, the use of the five
senses in the child development age without the purpose of
choosing the best one, but coherently using all of them.
The DYSAM approach is based on approaches such as the
Bayesian method, the Pierce abduction, the so-called:
Machine Learning, Ensemble Learning, and the Evolutionary
It was introduced to deal with the dynamical emergent
properties of complex systems, i.e., when
1.the system to be studied is so complex (processes of
emergence occur within it) that we cannot, in principle,
describe it using a single or a sequence of models,
refinement of the preceding one, and
2.the process of emergence gives rise to the dynamic
establishment of different systems, Multiple-systems (MSs)
and Collective Beings (CBs) introduced later.
Dynamic models model dynamical properties of a specific
DYSAM models change over time, i.e., the dynamic
acquisition of different, emergent properties and
properties of MSs and CBs as well.
It is not matter of different models of the same system but of
different models of the same systems having common,
interrelated variables, e.g., chemical, physical or
2) Multiple Systems (MSs)
A MS is a set of systems established by the same elements
interacting in different ways, i.e., having multiple
simultaneous or dynamical roles.
The role of single systems in a MS must be not confused
with that of subsystems related to different functions within
the same system.
Within the conceptual framework of MSs
concurrent/cooperative effects of different interactions
affecting the same elements perturb the effects of single
Moreover, the action of concurrent interactions may be
neither simultaneous nor regular.
The same interacting components may establish different
systems through organization or emergence and at different
times (i.e., simultaneously or dynamically).
Examples of MSs in systems engineering include
networked interacting computer systems performing
cooperative tasks, as well as the Internet, and electricity
networks (an unfortunate emergent property is the black-
out) where different systems play different roles in
continuously new, emerging usages.
3) Collective Beings (CBs)
CBs are particular MSs established by agents possessing a
(natural or artificial) cognitive system.
In CBs the multiple belonging is active, i.e., decided by the
component autonomous agents.
In the process of emergence of CBs agents interact by
simultaneously or dynamically using, in the model
constructivistically designed by the observer, different
Examples are Human CBs where:
(a)agents may simultaneously belong to different systems
(e.g., behave as components of families, workplaces, traffic
systems, as buyers, of a mobile telephone network).
Simultaneously is not only related to time, but also to agent
behaviour, considering their simultaneous belonging, and
their roles in other systems; and
b) agents may dynamically give rise to different systems,
such as temporary communities (e.g., audience, queues,
passengers on a bus), at different times and without
considering multiple belonging.
Concepts of MSs and CBs allow one to realize how
managing one influences elements and interactions
while establishing another system.
The usages in social systems
It is related to inter-disciplinarity when:
•a model of a discipline is used for another one by
changing the meaning of variables;
•a problem is transformed into another one such as
military into political; social into economical; and
geometrical into algebraic.
4) Emergence between Architecture and social
A line of research is studying architecture as the design of
suitable boundary conditions influencing emergence of
behaviour in human social systems (CBs).
This vision may help to clarify the role of architecture in
materializing structures leading to emergent social
The concept of field in classical Physics
In classical physics, a field is intended as made up of a
physical variable that has a value for each point in the entire
space and time, termed spacetime.
In other words, in a field a physical property is intended
available having a specific value in each point in spacetime
like the value of the temperature.
The value may in case depend on the distance from a
source -meant as generator of the field-.
Example of fields are, for instance:
the strength of the gravitational field in Newton's theory of
the strength of the electrostatic field in classical
the weather map, where the surface wind velocity is
described by assigning a vector to each point on a map.
Properties of specific bodies, like weight and electrical
conductivity, are examples of non-field properties.
In addition to the field of non autonomous elements we
should then consider other features peculiar to autonomous
elements, i.e., possessing cognitive system, such as:
•and cultural aspects
which are all interconnected and individually processed by
the cognitive system of each autonomous element.
In turn social fields act on social systems in a cybernetic
Social Their social
The resulting social field, or social environment, is
emergent from a variety of properties and actions having
The role of Architecture
The way of acting on the emergence of such social
fields through an explicit design of structures with
functional roles is typical of human systems.
Briefly, this role refers to artificial interventions such as
insertion of new structures and environmental changes.
The cybernetic loop mentioned above between social
systems and their social fields, including the one generated
by Architecture, generates dynamical and variable
continuity in both directions:
Social Their social fields
systems (materialised by Architecture)
a)Homes, architecturally designed to be inhabited in
particular ways so that we live in our homes as they have
been designed for;
b) Schools, organized into classrooms for each specific
subject separated from different disciplines, and then
didactics is influenced by the school design;
c) Hospitals, built to treat ill bodies (patients) to be repaired
/ cured and then medical treatments and activities are
affected by hospitals structures and design;
d) Roads shapes, street furniture, urban lighting, number of
doors in a flat, details in baroque architecture and music,
The structure of space made by Architecture both
represents and induces the social field within inhabitants
On the other side inhabitants behave by using such social
field. In this conceptual framework we may hypothesise a
process of self-architecture by social systems.
We mention the coherence in such social field between
different aspects such as architecture, design, fashion,
music and painting.
Self-design relates to the transformation of emergent
social properties, e.g., life styles and customs, into
structural constrains, aiming to acquire the same
properties as structural and no longer as emergent
5) From Growth to development:
the logistic curve
introduced by the Belgian mathematician P. Verhulst
(1804-1849) for the study of population growth
It represents changing from an increasing growing to a
We may consider the case when point e is reached.
a) Development as harmonic processes of growth;
b) Development as subsequent processes of growth;
c) Development as acquired emergent property of a
system of coherent processes of growths.
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