Untangling Complex Systems, page 5
strength and opposed the centralization of the political power, which was in the hands of the landed
aristocracy. The old aristocratic forms of government were transformed into new republican forms.
The City-States were established and consolidated; the Greek man was led to feel like a citizen.
In synthesis, the cultural, religious, socio-economic, and political environments of Greece in the
seventh and sixth centuries BC created the right conditions for the birth of philosophy, which is a
great revolution in the history of human thinking. The first philosophers had the merit of raising
“Really Big Questions” (RBQs)6 mainly regarding nature and the origin ( αρχή) of everything. They were named “natural philosophers” due to their interests. They endeavored to answer their RBQs
through rational and logical methods, particularly by intuition and induction. Their intuitions were
mere intellectual formulations of principles. Their inductions were based on all the information
gathered by their senses7 along with the practical and technical knowledge stored by their ances-
tors. For sure, some of the first philosophical RBQs were also arisen by our ancestors, during the
“Practical Period.” Answers were found through the myth, exploiting fantasy and religious beliefs.
On the other hand, philosophers proposed solutions to their RBQs, trusting just in their minds,
6 The expression “Really Big Questions” was coined by the physicist John A. Wheeler (1911–2008), who, in his career, formulated questions so broad and important to involve both physics and philosophy.
7 Some philosophers, such as Melisso from Samo (fifth century BC), denied any validity to the information gathered by senses, trusting only in mind.
Introduction
7
through reasoning purified from any superstition and prejudice. In some cases, they suggested solu-
tions and answers, which appear astonishing even nowadays. In fact, they are still valid in their
essence. For instance, Pythagoras and his disciples, between the sixth and fifth century BC, realized
that the key to understanding nature is mathematics. Everything in the universe is harmony and
number. A mathematical regularity exists everywhere.8 Empedocles and Anaxagoras (fifth century
BC) formulated what is known today as the principle of conservation of matter, stating that noth-
ing comes from nothing, and nothing can be utterly destroyed. Leucippus and Democritus (fifth to
fourth century BC) guessed that everything is composed of atoms and between atoms lies empty
space; atoms are indestructible; atoms have been and will always be in motion. Moreover, there is a
huge number of atoms and kinds of atoms.
With the birth of philosophy, the human journey to discovering the secrets of nature under-
took a second stage named the “Philosophical Period” (see Figure 1.3). Within the scope of phil-
osophical mentality, i.e., within the scope of its etiological rationalism (prone to search for the
cause of everything by reasoning), the knowledge of nature specialized, thus separating in different
disciplines. These disciplines were mathematics, geometry, astronomy, geography, and medicine.
The philosophers developed mainly theoretical aspects of the various scientific disciplines, over-
looking their technical and practical aspects.9 Through induction and intuitions, they formulated
postulates and axioms of the different scientific disciplines. For example, Euclid wrote the Elements
(around the 300 BC), grounding geometry and mathematics. Archimedes (third century BC) wrote
the Equilibrium of planes, providing the theoretical basis of statics. Ptolemy (second century BC)
composed a comprehensive treatise on astronomy of his time, titled the Almagest, and Galen (third
century AD) wrote the On the Elements according to Hippocrates exerting an important influence
over the theory of medicine until the mid-seventeenth century AD. The scientific knowledge maintained
its speculative-theoretical facet during the first part of Middle Ages. From the mid-eighth century
AD until the mid-thirteenth century, the Arabic culture, fed by both the ancient Greek and Latin
texts along with the Chinese and Indian intellectual sources, blossomed into its Golden Age. In the
Islamic Golden Age, there were some Muslim Philo-physicists who boosted the scientific inquiry.
A famous example is Ibn al-Haytham (also known under the name of Alhazen, 965–1040 AD)
whose main contribution was that of placing, for the first time, a particular emphasis on experiments.
Experiments are the ultimate ways for choosing between scientific theories that are under debate. 10
Through this brand-new approach, he made significant advances in the field of optics. The contact
with the Islamic culture favored an intellectual revitalization of Europe. The revival started in the
twelfth century and was sealed by the birth of the first universities. In medieval universities, students
were learning the liberal arts, which were grammar, rhetoric, and logic (called the Trivium) along
with mathematics, geometry, music, and astronomy (called the Quadrivium). These disciplines were
fundamental for a free citizen to study, and they were mandatory to gain access to the higher faculties,
that is law, medicine, and theology. Among the many important scholastics, some were distinguished
for their thinking about nature. Albertus Magnus (twelfth century), Robert Grosseteste (twelfth cen-
tury), Roger Bacon (thirteenth century), and finally William of Ockham (fourteenth century), all partly
influenced by the Islamic culture, triggered a paradigm shift in the scientific inquiry. They underlined
8 You may ask yourself if mathematics is either an invented ensemble of tools to be continuously improved or something real to be discovered. In my view, the best answer was proposed by Aristotle: the mathematical objects are neither real nor unreal. They exist in potentiality in nature, and our reason catches them by abstraction. The mathematical tools exist just inside our minds.
9 Of course, medicine could not be just an intellectual discipline because it always had to cure people of illnesses. However, in the “Philosophical Period,” medicine improved also from a theoretical point of view with the introduction of etiological explanations of diseases.
10 Some historians have described Ibn al-Haytham as a pioneer or “the first scientist” of the contemporary scientific method.
He established the experiments as proofs of scientific hypotheses. As Gorini (2003) said, “his investigations were based not on abstract theories, but on experimental evidence and his experiments were systematic and repeatable.”
8
Untangling Complex Systems
the importance of mathematics for understanding nature and stressed that the proof of any scientific
acquaintance should come from real experiments. This adhesion to the concrete evidence steered
William of Ockham to refuse any metaphysical hypostatization, i.e., abstraction of concepts such as
space, time, motion, et cetera. He introduced the principle of parsimony, well known as Ockham’s
Razor: Entia non sunt multiplicanda praeter necessitatem (“entities must not be multiplied beyond
necessity”). This principle recommends Philo-physicists to not to postulate unnecessary entities and,
among competing hypotheses, to select the one that makes the fewest new assumptions until evidence
is presented to prove it false. During the first part of Renaissance (on the whole spanning about two
centuries, the fifteenth and the sixteenth), there was the polymath Leonardo da Vinci (1452–1519)
who went on the new way traced by Ockham and the other scholastics cited earlier. Leonardo insisted
on the idea that just mathematics allows for the interpretation of the mechanical and necessary order
of nature. Moreover, he weeded out any animistic, mystic, and spiritual forces from empirical events.
Finally, he gave a significant contribution to the next scientific revolution by bringing mechanical11 and liberal arts to the same level of cultural dignity.
1.1.3 The “exPerimenTal Period”
Two thousand, two hundred years elapsed before witnessing the second gateway event in the human
journey to discovering the secrets of nature. This second gateway event was the formulation and
application of a mature experimental method. It took place in the Scientific Academies that blos-
somed in Italy during the seventeenth century and then spread to the rest of Europe.12 In the Scientific Academies, figures as diverse as natural philosophers and craftsmen started to collaborate by merging theory and real experiments. Together, they devised “exo-somatic” tools bringing great benefits.
In fact, instruments (1) extend the frontiers of human knowledge about nature, otherwise delimited
by the investigating power of our senses. (2) They avoid misunderstandings which could sometimes
derive from a blind trust on our sensorial perceptions. Finally, (3) they gain objective, reproducible
and universally valid responses from nature. With the instruments in hand, natural philosophers and
craftsmen could establish highly constructive dialogues with nature. They were asking nature if it
obeys their hypothesized theories and laws. If nature repeatedly and unequivocally assented, the
laws and theories were validated; otherwise, new ideas and models were needed. The experimental
methodology was first theorized and applied by Galileo Galilei (1564–1642) and then supported and
completed by Isaac Newton (1642–1727). Thanks to the great contributions of Galilei and Newton,
the “Experimental Period” begun (see Figure 1.3). According to the Hegel’s dialectic, 13 this third period can be conceived as the synthesis of the two previous stages: the “Practical Period,” which
was the thesis, and the “Philosophical Period,” which was the antithesis (see Figure 1.5).
During the “Experimental Period,” theory and practice walked hand in hand. Usually, natural
philosophers used to formulate a question and a possible answer. Then, they, along with artisans,
were designing experiments by devising suitable and reliable facilities. To collect unequivocal and
reproducible answers from nature about the validity of their hypothesis, the team of authentic Philo-
physicists used to “purify” the phenomenon, which they wanted to analyze, by isolating it from the
rest of the world. Moreover, natural philosophers started to describe the natural phenomena by the
11 Mechanical arts are activities requiring manual skills rather than only mental abilities.
12 The first academy focused exclusively on scientific knowledge was the Accademia dei Lincei founded in Rome in 1603.
In 1657, Prince Leopoldo of Tuscany, student and friend of G. Galilei, founded the Accademia del Cimento in Florence.
In 1662, Charles II of England created the Royal Society of London for the Improvement of Natural Knowledge, whose
Isaac Newton was first member and, then, secretary. This academy promoted the publication of the Philosophical
Transactions, which is the first example of periodic journal regarding scientific subjects published in Europe. Under the reign of Louis XIV, the minister Colbert founded the Académie Royale des Sciences. Many other academies were born
during the eighteenth century.
13 Georg W. F. Hegel (1770–1831) was a German philosopher.
Introduction
9
Experimental
period
Synthesis
Philosophical
period
Antithesis
Practical period
Thesis
FIGURE 1.5 The first three stages of the humankind journey to discovering the secrets of nature analyzed
through the lens of Hegel’s dialectic.
universal language of mathematics and geometry. As Galilei stated in his book titled The Assayer
(1623 AD), the universe “stands continually open to our gaze, but it cannot be understood unless one
first learns to comprehend the language and interpret the characters in which it is written. It is writ-
ten in the language of mathematics, and its characters are triangles, circles, and other geometrical
figures, without which it is humanly impossible to understand a single word of it; without these, one
is wandering around in a dark labyrinth.”
The new methodology to understand the secrets and the marvels of nature, proposed in the
Academies, brought about revolutionary discoveries. During the seventeenth century, the first
relevant results were achieved in astronomy. Nicolaus Copernicus (1473–1543), Tycho Brahe
(1546–1601), Johannes Kepler (1571–1630), Galileo Galilei were provided with accurate sextants, 14
quadrants, armillary spheres, and telescopes to study our Solar System. They discovered that the
Solar System is heliocentric and not geocentric. Moreover, the orbits of the planets are elliptical and
not circular, as believed before. Finally, the heavenly bodies comply with the same physical laws
as the terrestrial bodies. Therefore, the planets can stay in their orbits without being fixed to solid
spheres, just because they interact through the gravitational force, as Newton inferred. Newton
(1687) wrote a book titled Philosophiae Naturalis Principia Mathematica, which is considered “as
one of the masterpieces in the history of science.” 15 In the Principia, Newton laid out the foundations of what is nowadays known as the “Classical Physics.” He formulated the laws governing the
physical behavior of macroscopic bodies. Moreover, he invented calculus to rigorously describe
change and motion, through new mathematical notions such as infinitesimal, derivative, integral,
and limit. Finally, he formulated the four “Rules of Reasoning in Philosophy,” 16 which became the foundations of two important “epistemological pillars.” Epistemological pillars are platonic ideas
guiding the interpretation of natural phenomena and the formulation of axioms and postulates. The
first epistemological pillar is “Simplicity:” “Nature loves Simplicity.” Therefore, the truth is always
to be found in simplicity. It resembles the Ockham’s Razor. The idea of a “Simple Nature” inspired
14 Sextants and quadrants are instruments to measure angles; the armillary spheres were models of the solar system to demonstrate how it works.
15 Assessment extracted from “Reading the Principia: The Debate on Newton’s Mathematical Methods for Natural Philosophy from 1687 to 1736” by N. Guicciardini.
16 Remember that with the term “Philosophy,” Newton meant what we nowadays define “Science.” The term “scientist” was coined by William Whewell (1834) to indicate all those figures who dedicated their lives to the study of nature by using the austere and rigorous experimental method (since the seventeenth century AD).
10
Untangling Complex Systems
the reductionist approach in the scientific inquiry. Such an approach consists in describing a natural
system by decomposing it in its constituents and studying their properties, singularly. Finally, the
picture of the entire system can be reconstructed as a simple sum of the features of its elements.
The second epistemological pillar is “Uniformity:” “Nature is Uniform.” The natural laws, which
are valid hic et nunc (“here and now”), are true always and everywhere in the universe: they are
“Universal.” The idea of Uniformity, also known as Uniformitarianism, is at the core of any sci-
entific discipline, but in particular of geology. In fact, as proposed by the Scottish geologist James
Hutton (1726–1797), the same natural laws that rule the processes in the universe now, have always
been in action in the past and everywhere in the universe.
During the eighteenth and nineteenth centuries, the classical mechanics, formulated first by
Newton, was further developed and improved to such an extent that the reliance on it was almost abso-
lute. The confidence in the simple laws of classical physics favored the establishment of two further
epistemological pillars: the “Determinism” and the “Mechanism” (see Figure 1.6). The Determinism
is well epitomized by the statement written by Pierre-Simon Laplace17 in his A Philosophical Essay on Probabilities (1814 AD): “We may regard the present state of the universe as the effect of its past
and the cause of its future. An intellect which at a certain moment would know all forces that set
nature in motion, and all positions of all items of which nature is composed, if this intellect were also
vast enough to submit these data to analysis, it would embrace in a single formula the movements
of the greatest bodies of the universe and those of the tiniest atom; for such an intellect, nothing
would be uncertain, and the future just like the past would be present before its eyes.” In other words,
Laplace was advocating that since the natural laws are deterministic and known, if we could deter-
mine position and momentum of every particle in the universe at a specific moment in time, we would
be able to predict any subsequent event. The future is potentially predictable.
The fourth pillar, the Mechanism, sustains that everything in the universe, either inanimate or
animate, behaves like a machine. Also “vital” phenomena, like passion, memory, and imagination
“follow from the mere arrangement of the machine’s organs every bit as naturally as the movements
