Let's follow a thought with Mauro Guerra: who has never wondered, in recent times, whether the phenomena we are experiencing are not governed by turmoil and chaos? It almost seems that since the outbreak of the pandemic, the speed of events has undergone an unprecedented acceleration, at least compared to the last hundred years. The reality that surrounds us has acquired a different form, or perhaps it has definitively lost that same form to take on another appearance, becoming fluid and at the same time dizzying, in a succession of dramatic, but also recurring, events, irrepressible and, in a certain way, persistent.
First the wildfire propagation of Covid-19, a virus, an element of a few tens of nanometers capable of blocking and upsetting the entire planet, with the consequent interruption of the production and distribution chains, whose continuous work was for everyone an indisputable fact; finally, the exacerbation of inflation unprecedented in the last forty years. All this is increasingly accompanied by small and large financial crises and increasingly violent environmental disasters extending to different areas of the world. The anachronistic and absurd war, conducted at the behest of the Russian President in neighboring Ukraine, seems to represent the icing on the cake of a disruption to which we have become accustomed, a poisoned dessert served to us systematically for some time now. What is this bitter pastry called? Is it called chaos?
The Greeks identified it as an open space, a chasm, an abyss where darkness and obscurity reside, but it was Hesiod in Theogony (7th century BC) to attribute to Chaos, one of the primordial entities of mythology, with Gaea, Tartarus and Eros, the personification of the state of "emptiness", the darkness from which the cosmos, gods and men emerged. A few centuries later, with Anaxagoras and Plato, chaos takes on a meaning closer to what we know today as "disorder".
The two ancient philosophers classified it as the place of formless matter to which the mind (Join) was able to draw on it to create the ordered world: the cosmos.
Quantum physics also places chaos at the origin of the cosmos. It would have been a vacuum characterized by energy fluctuations, called It was from Planck (from the name of the German physicist Max Plank), i.e. the first 10 to -43 seconds preceding the expansion of the universe, the so-called Big bang which, according to modern science, dates back to 13,8 billion years ago.
In different eras the approaches to chaos change, but they seem to agree on some elements: the void, the darkness, the formless matter and the energetic variability, a kind of precipice before immersion in something different and clearer.
Mathematics has proven to be austere towards chaos and since the end of the 800th century, with the French mathematician and physicist Jules Henri Poincaré, it has attempted the study of chaotic phenomena, that is, the observation of dynamic systems that exhibit a sensitivity exponential with respect to the initial conditions. The mathematical analysis of these manifestations took shape in the following century through the studies, among others, of the American mathematician and meteorologist Edward Norton Lorenz, who, after the war, developed the Chaos theory. The latter, if cut with an axe, can be reduced to the concept of the "butterfly effect"..
The beating of a butterfly's wings, therefore an insignificant event at the beginning of a process, can influence its course so that its consequences change exponentially over time.
La Chaos theory has opened the doors to a world dotted with apparently causal variables. In fact, at least according to mathematics, they are much more predictable than one might think, because they are governed by deterministic laws, as Mauro Guerra, Director of the Lugano Pension Fund, mathematician and author, explains to us in 1985, at the University of Zurich, of a thesis entitled Propagation of Chaos and non-linear diffusion processes.
«In reality, what is summarily called “Chaos Theory”, and which rightly dates back to the early 60s, should be considered rather as the “Mathematical definition of chaos”. The latter was formulated by the Polish polymath and statistician Mark Kac, through a classical mathematical approach. It is interesting to observe how in mathematics chaos has a positive meaning, not a negative one. In fact, if initially and under certain conditions the interaction between particles, i.e. "disturbances" described through mathematical functions, causes them to lose their initial independence, we note how, with the passage of time and with the increase in the number of interactions, independence is re-established. This is "something" that is non-intuitive, perhaps even apparently contradictory. In mathematics, therefore, chaos means re-establishing independence.
In the 80s, at the time of my studies in mathematics at the University of Zurich, I became fascinated by stochastics (a set of techniques and theories belonging to the calculation of probability) and its innovative approach. Precisely in that period, within the Zurich school, there was considerable excitement regarding the extension of this branch of mathematics. Famous mathematicians from all over the world were involved and, in particular, from the Japanese school, such as Kiyoshi Itō and Hiroshi Tanaka, precursors in the work on the propagation of chaos through a probabilistic method and not through classical analysis.
In the wake of those events I was assigned the topic of my degree thesis: the proof of the conjecture (in mathematics a conjecture is defined as a conclusion or proposition formulated on a provisional basis, without proof) by the American mathematician Henry McKean of MIT, who, in collaboration with Itō, he had treated the propagation of chaos, but without a rigorous demonstration typical of the Japanese school. The demonstration fell to me, burdening me with particularly complex and demanding diploma work, but which allowed me to give my contribution to the evolution of stochastic research."
The so-called "Chaos Theory" has been applied over the years to many sectors, from meteorology to finance (in risk analysis and beyond), passing through the social sciences. However, you don't believe that there are points of contact between mathematics and other disciplines, just as you contest the link between mathematics and philosophy, is that right?
«I am a formalist, inspired by the school of Nicolas Bourbaki (heteronym with which, starting from 1935 and substantially until 1983, a group of high-profile mathematicians, mostly French, wrote a series of books for the systematic exposition of notions of advanced modern mathematics ed.) and therefore for me mathematics is independent of any relationship, extraction deriving from the physical world. It is a scaffolding in itself, a closed system that feeds itself. It is the physical world that draws on mathematics, not the other way around. An example in this sense is computational sciences. In fact, the evolution of large computers did not lead to a revolution in mathematics; if anything, it was mathematics that determined the evolution of computer sciences. Today, it is the mathematicians with the most advanced theories who provide the most important contributions to artificial intelligence.
To return to the concept of chaos, we must stop conceiving it in its philosophical representation, because it is wrong. As I explained previously, the definition of chaos is the re-establishment of independence, under certain conditions, after an infinite number of particle interactions."
The disturbing and destructive phenomena that we have been witnessing for some years, such as the spread of the pandemic, natural disasters, global warming, particularly violent conflicts in many areas of the world, financial collapses and economic crises, push us to question ourselves. What contribution can mathematics and, in particular, "Chaos Theory" make in addressing these problems?
«Right now we are faced with many non-linear diffusion variables, such as pollution, world population growth, Covid, etc., which, obviously, interact with each other.
The question we ask ourselves is the following: will it be possible to re-establish chaos, that is, independence, reorganization? Mathematics answers in the affirmative, since at a certain point all these ties, these interactions of social, political, geographical and much more, tending towards infinity, will fail to rebuild an independence and therefore a restructuring, a starting condition optimal.
The turbulence we are experiencing, especially from an environmental point of view, must lead us to review the basic concepts of the economy, finance and our way of life in a scientific and non-dogmatic way. It's nothing new. The Romanian mathematician and economist Nicholas Georgescu-Roegen, one of the precursors of the idea of degrowth, was already talking about it in the 70s, arguing that sustainable growth is an oxymoron. In my opinion, this type of study and approach to the ecological question must be rediscovered, so as to better interpret the contemporary world and find solutions.
I am convinced that mathematics is experiencing a new Renaissance, an innovative phase in many areas, a bit like the one I was able to experience firsthand in the 90s in the world of finance through risk management.
The difficulties already highlighted more than fifty years ago by the Club of Rome (non-governmental association founded in 1968 and composed of scientists, economists, business women and men, civil rights activists, senior international public managers and heads of state of all and five continents. The Club of Rome promoted the "Report on the limits of development", identifying the main problems that humanity would have to face - ed.), they are presenting themselves with a devastating magnitude, they touch the very concept of growth , sustainability, including that linked to investments and financial techniques. For now too little has been done in this sense and what exists refers to traditional models which in many cases are artfully constructed to defend the status quo.
Substantial development is therefore more necessary than ever to orient ourselves in the future, as well as representing a stimulating challenge especially for the new generations. It is important to understand that what is happening in the world, and first of all, in the context of the climate emergency, from the policies promoted by different governments to the actions of activists on the streets, it is possible to translate it into mathematical theory. Evidently, as a mathematician, I intend and hope for a rebirth of the revolutionary spirit, in the scientific sense, which animated the Club of Rome.
In our small way, we too, at the Lugano Pension Fund, are actively committed to sustainability linked to investments, observing and implementing our policy according to ESG (Environmental, Social and Governance) criteria. This is a first step, without forgetting Georgescu-Roegen's warning!
In this regard, we refer to chapter 7 of Management report of the Lugano Pension Fund (CPdL) to link https://www.cpdl.ch/it/rapporto-di-gestione/rapporto%202022.
