Systems, complex systems, and intelligence: An educational overview

GIANFRANCO MINATI

Italian Systems Society http://www.airs.it

Via Pellegrino Rossi, 42

ITALY

analytic approach and to forms of reductionism. We outline aspects of the science of complexity such as

coherence, incompleteness, quasiness and issues related to its modeling. We list and consider properties and types

of complex systems. Then we are dealing with forms of correspondence that concern the original conception of

intelligence of primitive artificial intelligence, which was substantially based on the high ability to manipulate

symbols, and of those of a complex nature that consider emergent processes, such as inference, the learning,

reasoning and memory. Finally, the recognition and acquisition of forms of intelligence in nature is explored,

with particular reference to its emerging systemic processes.

Key-Words: - Coherence, Complexity, Emergence, Incompleteness, Intelligence, Quasiness, Self-Organization.

Received: July 17, 2021. Revised: February 24, 2022. Accepted: March 27, 2022. Published: April 21, 2022.

problems of various types, such as those centered

around interdisciplinary scientific education. The

article concludes by hinting at the topic of

intelligence, discussed in relation to complex

systemic properties, up to the important subject of

artificial intelligence. In this work, we consider the

concepts of system and complex system that are

widely used in everyday language, which involves

the examination of diverse topics ranging from

systemic pathologies to computer systems and

comprehensibility, and reproduction. The complexity

is considered to be negative attribute.

Systems are interesting because they may acquire

properties that are not reducible to those of their

components; for instance, in the functioning of

electronic and electro-mechanical devices. Unlike

objects, systems do not possess definitive properties

such as a weight, or results, for example, cooking or

a flame from the burning of a candle. The engine of

systems is the process of interactions between its

states that depend on that of the other elements.

Systems are intended to acquire the same iterated

property that characterize the whole system, i.e.,

electronic components when interacting establish a

system having the same property such as of being a

computer, a smartphone, or a television. When the

composite elements cease to interact, the system

degenerates into a set of components (Section 2).

and they continually occur within them. Contrasting

with systems, complex systems acquire a sequence of

multiple properties that arise in variable ways and

they have significant levels of coherence. Complex

systems are established via multiple interactions, as

in processes involving self-organization and

emergence. In short, self-organization in the

populations of interacting elements can be

understood as the prevailing formation and

maintenance of synchronizations in terms of

intended to be activated and maintained by the

presence of particular environmental situations, for

example, self-organization by topological constraints

and dissipation for vortexes of liquids in pipes or the

temperature differences in tornadoes, while

emergence by properties of the interacting elements

such as their available mobility, ability to fly, innate

and cognitive abilities (Section 3).

The processes of emergence, and their acquired

properties, are robust when perturbations are applied.

of equivalences and partialities, in which the

multiplicity of coherence is not reduced to a single

synchronization. Examples are flocks of birds and

swarms of bees that continuously present themselves

in different forms, while maintaining their

consistency and acquiring intelligent-like behaviors,

for example in defense from predators. The topic

becomes increasingly interesting when the area of

study is not just about birds and insects, but the

collective behaviors of people such as those observed

emergence manifests itself in an innumerable variety

of processes that correspond to the keeping of

complex systems; to acquired variable, various

properties to be considered in dealing (e.g., inducing,

emergent nature of the acquired properties, which are

attained by the complex systems, enables their

robustness, thus they are able to resist perturbations,

(Section 4).

Among the properties that are acquired by complex

systems, we consider forms of intelligence, such as

the intelligence of collective behaviors in terms of the

present in different forms while maintaining their

As a second option, intelligence as a property of

nature that enables, for example, the occurrence of

chemical reactions, phase transitions, and constitute

fields. Also of interest is the ability to establish

fractality that allows for the availability of large

surfaces in small volumes, for example, alveoli of the

lungs. A third option to consider is emergence of

generic intelligence, i.e., not related to specific

behavioral factors but ones that are available to be

applied to any problem or even to itself (Section 5).

2 Systems

The concept of a system is introduced by the

biologist-mathematician Ludwig von Bertalanffy

(1901–1972) in his most famous book [1]. The

interest in systems may arise because such entities

have the ability to acquire properties that are not

completely) on those of the others. More precisely,

the interaction can be considered as a relationship

when specified by fixed relationships between the

entities (such as temporal -synchronization- and

quantitative -proportion-). One way to understand the

interaction process is to consider it as an ongoing

interaction, for example as an exchange of

materiality in economics, or energy and information.

In the case of the action-reaction effects, such as for

the collisions between balls and activations via

contextualized form of relationship (for example, the

collision of two balls affected by their irregularities

due to, for instance, wear). In the most specific case,

the interaction is intended to occur between entities

that are endowed with autonomy, when the inter-

exchanged (both matter and energy) and information

(either inter-exchanged or detected) is autonomously

processed by the entities, such as when birds of a

flock cognitively decide their reaction based on the

reciprocal positions, speeds, and directions that they

irregular combinations of the various possibilities, in

a multiple and time-varying way with different levels

of equivalence until initiation of a new non-

equivalent behavioral phase [2].

The components are considered as such in the case

of natural processes, which are either intended by the

observer to be systems (for example, solar, digestive,

ecological, reproductive systems, flocks, swarms,

and anthills) or designed (components of electronic,

mechanical, and hydraulic systems). The properties

they are continuously acquired. This is a matter of

contrasting transformation with interaction. In the

case of transformation, the elements (the

components) change throughout the processes in

terms of various phenomena such as thermal,

chemical, and electrical. These are in reference, for

example, to the science of materials (think of the

flame of a candle). In the case of interactions, the

interaction process is assumed to be of interest when

it generates systemic properties. In fact, the

interaction process provides the functioning for

devices, for instance, acquiring electronic

characteristics. The interaction between the elements

occurs via the power supply. When this ceases, the

longer powered. The properties that were acquired

become potential, are lost. Later, we will see the case

of complex systems [3, 4], in which the interactions

between the components cannot be prescribed.

The issues relating to the concept of property are a

delicate one. We will limit ourselves to its use at the

current level in cultural usage, as it is not the purpose

of the article to extend it further. Let us mention that

the detectability of the properties requires, in turn, the

availability of properties and the ability to relate to

detected properties, alleged constituted systems, and

their acquired detected properties intended as

systemic.

2.1 Systems epistemology

f(x), is given by the validity of additivity: f(x + y) =

f(x) + f(y) and the homogeneity: f(αx) = αf (x) for

as an exponential and trigonometric equations.

Trivial systems have fixed spaces of becoming (with

few, limited degrees of freedom, i.e., in terms of

variables such as speed, position, and temperature

that are necessary to describe a phenomenon. In

complex systems we consider a number of these

variables, and their eventual change, in the course of

the becoming of the phenomenon or process) and

variable degrees of freedom), there are numerous

properties that can be acquired, and the components

are identified as appropriate (suitable for constitute

systems). Multiple and different interactions occur,

which can be represented as sequences of irregular,

linear and, mainly, nonlinear relationships. We will

However, at this point, we detect the peculiarities of

systemic becoming with fundamental

epistemological effects. Starting from what

actually, logically, and mathematically, and then

be ‘put together.’ The second condition is that the

relations describing the behavior of parts be linear;

only then is the condition of summativity given,

i.e., an equation describing the behavior of the

tota1 is of the same form as the equations

describing the behavior of the parts; partial

processes can be superimposed to obtain the total

process, etc. These conditions are not fulfilled in

the entities called systems, i.e., consisting of parts

which are ‘nontrivial’ [7] (Simon, 1965), i.e.,

nonlinear. The methodological problem of

systems theory, therefore, is to provide for

problems which, compared with the analytical-

summative ones of classical science, are of a more

general nature.”

The classical analytical approach is based on the

generic conceptual possibility that enables a

breakdown into different parts, which are assumed to

form the overall problem when recomposed through

point, we can observe how non-trivial systems are not

decomposable, non-linearly recomposable, and their

properties are not attributable (for example,

deductible) to those of their constituent elements.

a fundamental level without interactions, there is the

definitive explanation in or dealing with the

macroscopic systemic realm does not resist.

However, we are indebted to the analytical approach,

which has forged science for centuries and it is still

effective for addressing non-systemic problems. It is

also necessary to detect its inadequacy when it comes

to systems or be used in a methodologically adequate

way as for simplified, local, and temporary aspects.

The problem on one hand is to recognize the systemic

level means considering the levels of description of

the components and adequate (detected, supposed,

inferred) interaction mechanisms (combinations of

interactions, see [9]) that can possibly be multiple

and variable. This is the case of quasi-systems, which

are considered later for specific complex systems.

While the analytical approach inherently contains the

assumption of the existence of an optimal and

objective level of description, this does not occur in

the systemic approach. In the analytic vision, for

study, i.e., the system, as continuously being

established by interacting structural multiplicities.

The analytical conceptual world has assumptions

that are often considered as paradigmatic of the

scientific approach itself. And indeed, when it is not

a question of systems and their acquired properties,

they are. There are probably other cases in which

such assumptions do not hold, beyond systems, as in

the world of quantum physics, but this is not

examined here. Some characteristic assumptions of

the only approach. Completeness can be understood

as corresponding to the fact that a phenomenon or

process has a finite number of degrees of freedom

(which can be completely described by a finite

potential completability such as in so-called grey

systems [10]. A completeness with an infinite number

of degrees of freedom can be considered as

corresponding to incompletable incompleteness.

However, it should be considered how prescribing,

for example, constraints can mean imposing

innumerable (which is the incompleteness) ways to

respect them (refs. [11], [12], pp. 47-51).

Speaking of incompleteness, we cannot forget to

mention fuzzy systems for which the constituent

incorrect search keywords. The problems, in

principle, if we have been able to formulate them,

could only be resolvable. Otherwise, it remains a

problem that is waiting for a solution or will have

extreme curiosity in the event of apparent

irresolubility. This, the solubility, as Warren Weaver

(1894-1978) said, for example in [14], concerns the

problems of simplicity that can be completely

described by a few variables (with limited degrees of

freedom) and with a few differential equations, such

freedom, which are intractable considering the

individual entities involved. Appropriate approaches

were identified as those involving statistics and

probability, of a macroscopic nature, with a search

for adequate overall indices, as in thermodynamics in

the study of gases in which the phenomenology of the

interaction is unspecified (for this reason, Weaver

speaks of disorganization). Accuracy was transferred

to a consideration of suitable indices such as

pressure, temperature, and volume. Accuracy would

variables are “…interrelated in a complicated, but

nevertheless not in helter-skelter fashion…” [14, p.

539]. The latter is within the context considered by

Bertalanffy [1, p. 34], when he writes:

thermodynamics. In contrast, the fundamental

problem today is that of organized complexity.

Concepts like those of organization, wholeness,

directiveness, teleology, and differentiation are

alien to conventional physics. However, they pop

up everywhere in the biological, behavioral and

social sciences, and are, in fact, indispensable for

dealing with living organisms or social groups.

Thus a basic problem posed to modern science is

a general theory of organization. General system

complicated, but nevertheless not in helter-skelter

fashion in terms of quantitative properties such as

coherence, correlation, scale invariance, power laws,

self-similarity, network properties, chaotic

properties, and polarization (see section 4.5). We

only mention here how this radically changed the

naive concept of law considered in the problems of

simplicity. In this regard, we cite what the great

physicist Richard Feynman (1918-1988) wrote on the

characteristics of physical law under the influence of

from there. Tomorrow I may forget that this is

true, but remember that something else is true, so

I can reconstruct it all again. I am never quite sure

of where I am supposed to begin or where I am

supposed to end. I just remember enough all the

time so that as the memory fades and some of the

pieces fall out I can put the thing back together

again every day” [15, p. 45].

“In physics we need the Babylonian method, and

not the Euclidian or Greek method.” (Ibid., p. 47)

mathematics, based on set theory with an emphasis

on axiomatics and formalism. The end of this project

was a manifestation of the diminishing effectiveness

properties that are invisible to the analytical approach

except as partial completeness, approximation, and

imprecision, partial solubility or relativism. On the

contrary, as we will see when dealing with complex

systems, the incompleteness is required to allow for

the establishment of innumerable equivalences,

evolutionary options for the system,

interchangeability of roles, multiplicity, simultaneity,

overlap, dynamics of levels of loss, and recovery of

properties, as necessary for the establishment of

properties such as disassembly and reassembly of

systems, the linearity (or in any case reversibility) in

a context of relationships considered fixed, isolable,

explicit, and, for example, always completely

symbolically representable (see section 3.3, at the

point Computational Emergence, for sub-

symbolicity). In essence, this reductionism ignores

and denies the establishment of properties by the

interacting elements in the system that are not

linearly attributable to the properties of the elements

importance of confusion lies in the fact that its

validity, such as acting on the symptoms, i.e., on the

elements, is assumed and it is believed to act

identically on the system reduced to the sum, linear

compositions, iteration, or amplification of the

elements.

We end this section with an epistemological

reference to the contrast between objectivism and

constructivism [17-19]. The above, in particular the

incompleteness, multiplicity of equivalences,

here, but they are treated by a great variety of authors.

The objectivistic approach consists in retaining the

existence of the objective reality, about which we

must discover how it really is. The constructivist

would attempt to discover how the reality of nature

really is. While, in the case of constructivism, the

experiments would be understood as questioning

nature answering by being made to happen. Thus, the

answers depend on the questions and without

questions there are no answers. Furthermore, there

are facts or events that can be understood as answers

to questions that should be invented in such a way as

to transform facts into answers. Objectivism

conceives the knowledge as independently possessed

real.

Constructivism conceives of knowledge as a human

activity of interaction, which has emergent, acquired,

and effective properties. Disciplinary relativism is

replaced by a coherent and consistent multiplicity;

the approaches are spontaneously, inevitably

interdisciplinary. There is interdisciplinarity when

the problems, solutions, and approaches of one

discipline are used for others. For example, giving

different meanings for the variables of a set of

problems that are simultaneously physiological,

biochemical, physical, psychological, social, cultural

(for example, refusing treatment for any reason),

hygienic, alimentary, religious, environmental,

stress-related problems, and many others. It is not a

question of aspects of the medical problem, as

considered by objectivism, but of components

establishing the systemic medical problem that

cannot be disassembled in them, which must be

addressed by avoiding the reductionist approaches.

as for when the Earth is considered flat by consulting

a map for short distances.

complex systems

Let us begin with a quote from the English

philosopher George Henry Lewes (1817-1878), who

published a collection of five books between 1874-

1879 under the general title: Problems of Life and

Mind. He wrote:

“Every resultant is either a sum or a difference of

the cooperant forces; their sum, when their

directions are the same - their difference, when

their directions are contrary. Further, every

things of unlike kinds... The emergent is unlike its

components in so far as these are

incommensurable, and it cannot be reduced to

their sum or their difference in so far as these are

incommensurable, and it cannot be reduced to

their sum or their difference” [20, p.414].

In 1923, the British psychologist, naturalist, and

academic Conwy Lloyd Morgan (1852-1936)

introduced the concepts of emergence and emergent

evolutionism [21]. During the same period, the

biologist, writes:

“The meaning of the somewhat mystical

expression, ‘the whole is more than the sum of

parts’ is simply that constitutive characteristics are

not explainable from the characteristics of isolated

parts. The characteristics of the complex,

therefore, compared to those of the elements,

appear as ‘new’ or ‘emergent’.“ [1, p. 55].

The ’emerging‘ attribute was considered as a

synonym of ’new’ and ’unpredictable‘, and

proposed the construction of a theory of emergence.

introduced, linked, and subsequent to that of self-

organization [25, 26].

3.1 Self-organization

Self-organization processes can be understood as

consisting of a 'regular' sequence of property (such as

behavioral) changes of the collectively interacting

constituent elements, when their change over time is

predominantly regular; for example, in cases when

they follow an invisible organization. One can

imagine the establishment of configurations of

elements, their shapes, and overall behaviors, which

are in turn predominantly repeated and mainly

synchronized with each other (see Fig. 1). Self-

organization can be understood as a multiple and

variable distorted (linearly and nonlinearly, as

appropriate) amplification of a collective scale of

overall individual behaviors. Examples are the

formation of liquid swirls in pipes via dissipation;

regularity in the formation of queues in a traffic flow;

collective beings [29], such as those given by the

regular repetitiveness assumed by a swarm of flies

around a fixed light and the behavior of seagulls that

regularity of shapes within organisms, such as snail

shells.

Self-organization is linked to processes of self-

similarity, in which the global properties are the same

(precisely the same is only for geometric objects,

elements have usually the same nature, with

reference to the previous examples this includes flies,

gulls, vehicles, or molecules within liquids. This

means that everyone (or everything) reacts in an

'identical' manner, albeit with differences in times

and parameters, when certain external influences and

constraints are applied, such as shape and sections of

the pipes; shape, sections and height difference of the

roads; and stable action-reaction for flies around a

fixed light. This is the main synchronization source.

behaviors.

3.2 Emergence

The processes of emergence [30] can be understood

as the occurrence of multiple, different, simultaneous

sequences of self-organization processes partially

and dynamically involving same elements, when the

corresponding multiple acquired dynamic structures

are coherent, i.e., they maintain the predominance of

the same properties, despite the adoption of multiple

variable times and durations; interesting the same

elements having to play different roles. The

emergence gives rise to systems that are not just

static systems, since they are not always the same

system and also constitute other temporary systems,

i.e., quasi-systems, see point 2.2. Like flocks and

swarms that are constantly changing in structure.

In short, this emergence [35] is the factor that

characterizes the formation of complex systems and

provides the nature of their incompleteness and

dynamics and the quantity of detectable,

simultaneous processes of emergence that occur

within the system, by the properties of their

sequences (such as regular, partially regular, and

random), by their suspension and restoration, and by

their simultaneous influence on other elements or

their clusters [12, pp. 253-286]. Cases include

collective systems, collective beings that are

established by autonomous entities whose behavior,

in addition to the context seen in self-organizations,

to chemical signals or effects based on acoustics or

optics (as for stigmergy introduced later), as in the

following examples. Specific examples are anthills,

termite mounds, flocks, swarms, cities, herds,

schools of fish, and markets. These collective beings

acquire properties such as shapes and behaviors, e. g,

swarm intelligence considered later: sociological,

ways of expanding and consuming resources by

cities; and prudence, euphoria, or stability by the

financial markets. As we will see the emergence, the