Chaos and Cosmos
Our ancestors discovered in the world of experience a rational order or “cosmos” that allowed them to understand natural phenomena. Thanks to the scientific paradigm shift of the 20th century, chaos theory was developed. How do cosmos and chaos come along at the light of contemporary science?
Let’s look at the children, let’s see them play. Running from one side to the other, climbing, swinging. When we are girls and boys, the excitement of the novel, the healthily risky, is what most amuses us and attracts our attention. With time, we lose that capacity for astonishment and with it we become more and more insecure and fearful. Adults avoid the kind of experience we looked for as infants: novelty, imbalances, surprise, loss of control.
The bad news is that we live in a complex society in which it is very difficult to steer. We constantly experience contradictions and uncertainties. For example, at work, the month in which we make the most effort is not the month in which we do the best. Surprise has taken over, uncertainty grows about what happens and does not happen, and with it insecurity arises about what I am and what I am not, about what we should and can do and about what is not convenient for us to do. We live in a world without certainties, in which there is a generalised rule of not knowing what to expect. It seems that chaos has taken over everything.
The words chaos and cosmos are not precisely new. For the ancient Greeks chaos was inherent in the universe and everything that exists came from it. It is a concept similar to that of Buddhist emptiness. According to Greek myths, Chaos gave birth to the black Night and the Erebo, the dark and unfathomable region where death dwells. Night and Erebo, physical darkness and metaphysical one, these two children of primitive emptiness joined together to produce Love. In this way, compassionate love arises from the union of two negativities. Then Love originated Light and Day.
This myth is interesting because love emerges from darkness. In that sense it resembles the Taoist concept of yin, which is sometimes associated with evil and more correctly with darkness, but it is also the feminine, loving side. Then Light and Day arise. Again we have its Taoist counterpart, the yang (male, light), but it is also attractive to associate this myth with our own western mythology. Indeed, in monotheistic religions, God is love and creates, from chaos and emptiness to the Light and the day. The Light, with uppercase, because it is not only the electromagnetic wave or a mere flow of photons, but the Enlightenment, the possibility of reaching total clarity.
But unlike monotheism, for these early Greeks, as well as for the Eastern cultures, divinity is not only masculine and consequently, although Love creates Light, the Earth (Gaia) is born of Chaos and in turn it begets the sky (Uranus), sometimes covered with clouds, sometimes starry. Gaia and Uranus again remind us of their Chinese equivalents, yin and yang, respectively.
Later, in ancient Ionia, in the Aegean Sea, around the fourth century of the Christian era, arises the most abstract concept of cosmos understood, from that moment on, as a harmonious order that was created from the initial chaos. In this way, this new Aegean culture begins to decant a new type of mythology more abstract rather than poetic, mythology that over time would become philosophy and from which, as a prodigal daughter, would detach the slope that in the beginning was called “natural philosophy” and that today we know by the name of science. Consequently, both philosophy and science developed thanks to the fact that these ancient men and women discovered a rational order or “cosmos” in the world of experience and natural phenomena. Thanks to this, the Universe can be known, because there are regularities in nature that allow us to reveal its secrets. Without this regularity, nature would be unpredictable. However, this does not happen, since there are laws to which it must necessarily obey and which allow us to study and understand it.
When Renaissance thinkers retook the reins of the abandoned chariot called natural philosophy, they returned to sustain themselves in this primordial “myth”. The Universe or Cosmos is predictable, in theory, since it is ordered. Thanks to Newton’s influence this “mythology” is consolidated with the name of mechanicism, a philosophy that played a preponderant role in establishing the predominant criteria in culture from its time to the twentieth century.
In short, for mechanistic thinkers, if one could theoretically establish the position and velocity of all the particles of the Universe, one could determine, through the simple application of the laws of Newtonian mechanics, the future behaviour of all of them and, thus, of the Universe itself. The important thing here is the essentials of reasoning, not its practical application since that would be impossible. The important thing is that in theory that would be so, regardless of whether someone does it or no one ever succeeds in doing it. Consequently, the future of the Universe is determined by its present and the present, in turn, by its past. For mechanists, the invisible hand of God disappears, or, at most it gets relegated in this mythology to the very beginning, to the creation. God only establishes the initial conditions and the “rules of the game”. From there the Universe moves only and “by simple inertia”, not being left with an alternative. Cosmos comes to mean fatality, the end of free will. At least that would be the reading we would make from the mechanistic myth.
God at the casino
The 20th century had to come for this Cosmos to collapse all of a sudden. The cards below collapsed and behind them the immediately superior cards, in a catastrophic sequence, until they collapsed the entire castle of Newtonian mythology. Quantum mechanics was instituted in its place, and during that stage many physicists could not believe the conclusions they reached. Some of them went so far as to exclaim, “It’s as if the ground under our feet had been removed”. Chaos had returned and this time, it seems, to stay.
Albert Einstein, who — contrary to what many think — did not receive the Nobel Prize for his famous Theory of Relativity but for his contribution to quantum mechanics, was — curiously enough — always uncomfortable with the collapse of mechanicism. Quantum physics revealed the random character of the ultimate nature of the Universe and, with it, cosmos became chaos. The Universe ceased to be an immense winding clock, and became a roulette wheel. For this reason, Einstein once sentenced “God does not play dice”. However, quantum mechanics remains to this day the most exact, proven and verified scientific theory that has ever been developed and, therefore, the last word in physics is that God does indeed play dice with the Universe.
This discovery could make us think that we have gone backwards, that we will have to return to that time when nothing could be anticipated. The idea that the Universe is intrinsically chaotic could make us believe that everything is possible, from an elephant giving birth to a baby fly to people passing through the walls. That is not so, since chaos does not mean disorder but “complex order”.
Indeed, according to quantum mechanics there is a probability and therefore there is the possibility —at least in theory — of a person passing through a concrete wall, a phenomenon which is explained by the so-called “tunnel effect”. What happens, in practice, is that this probability is so ridiculously small that it becomes unfeaseable. Again, the important thing here is the essence of reasoning: in theory there is a certain possibility of going through the wall, even if it never happens, it is something that could happen at any given time, maybe greater than the age of the Universe. This is only an average of all possible times, it is an intermediate point between optimistic and pessimistic cases, but the possibility is always there and, if we are extremely optimistic, we might think that we will witness such a phenomenon; call it beginners luck!
The Universe is a roulette wheel and therefore the physicist can no longer predict in which case the ball will fall, he can only tell us what is the probability that we have of this or that happening. Nor can it tell us how many balls we should spin one after another until we win, it can only tell us — on average — how long we should wait to see a hit. Therefore quantum chaos does not mean complete freedom. Quantum physics can make predictions, it’s just that these are probabilistic and not deterministic in nature, as it was the case with classical physics and mechanicism.
This quantum uncertainty played a vital role in the “creation” of our universe. When all matter and energy were concentrated in a singularity, before the Big-Bang, there were no possible distinctions in that monolithic totality. The diversity that we see today, and that mainly translates into the non-uniform distribution of matter in space, is due to the fact that during the Big-Bang the laws of chaos operated. Had it not been so, the universe would have simply become a sort of “giant singularity,” an immense uniform and homogeneous mass of matter-energy; nothing like the galaxies, stars and planets we know. Zero possibility of life, in such a universe as monotonous and sterile as the void itself.
The butterfly effect
The story that over time has become almost a legend goes like this: in 1963 the meteorologist Edward Lorenz gave a talk whose title was as follows: “Did the flapping of the wings of a Brazilian butterfly create a tornado in Texas?” Lorenz had developed a complex mathematical model to predict the weather. He entered certain values through the keyboard of his computer and on the screen obtained a result. The idea was that he could enter into the system the current weather conditions and a certain amount of time to consider. The system, then, made the prediction of how the meteorological weather would evolve in that lapse. In this way, in principle, the model would make it possible to predict, in the light of how the weather had been on Monday, what would happen on Tuesday, Wednesday and so on. Undoubtedly, the larger the time gap, the less reliable the prediction became.
Lorenz discovered that the model was very sensitive to initial conditions, meaning that if Monday’s temperature or atmospheric pressure changed only a tiny fraction, the weather forecast that the system would make would change drastically and noticeably. It was as if the presence or absence of a butterfly on Monday could result in the occurrence or not of a storm on Friday. From that moment on, the term “butterfly effect” began to be used to refer to any system where this high sensitivity is present. Another way of referring to these chaotic systems is through the denomination of complex systems or non-linear systems.
One very important thing is that in a non-linear system — as with the quantum Universe —not everything can happen. No matter how chaotic a system may be, every time one processes the same initial data with absolute accuracy, the system systematically throws the same output. The unforeseen chaotic effect occurs only when the input conditions vary, albeit very little. In other words: the system is chaotic but this does not mean that it is random or completely free.
It is precisely this characteristic of lack of complete freedom that allows us to glimpse a certain degree of order within the chaos. A non-linear system may seem strange to us, but it remains predictable, strictly speaking. Scientists, such as Ilya Prigogine, Nobel Laureate in Chemistry in 1977 and deceased on May 28, 2003, studied the mathematical nature of non-linear systems and used a technology that could only be relied upon after quantum mechanics was developed: computers. With them it is possible for the first time to obtain graphs for non-linear systems.
We have all seen a histogram once. It is the typical line graph used to represent the evolution in time of the share price or the temperature of the sick. For a non-linear system what is obtained is visually chaotic. The graph looks like the lines drawn by a seismograph during an earthquake. You can hardly see anything clear in it. At best, it helps us to observe the maximums. This type of graph was therefore of little use to researchers of the nature of chaos. Instead they preferred to use other special graphics called “phase space”.
That strange attraction
Science and technology come together in a virtuous circle. As is well known, a virtuous circle is the same as a vicious circle, only with favourable rather than unfavourable results. The virtuous circle of science and technology operates as follows: science helps technology outperform itself and technology helps science to reach new discoveries.
That is what happened, for example, when quantum allowed microchips to be made. Thanks to this, scientists had computers with an extraordinary power of routine calculation. Operations that with paper and pencil can take hours, a computer performs them with absolute precision and in fractions of a second. Before computers no one had ever done the experiment of obtaining a phase graph for a non-linear system, basically due to the enormous amount of mathematical operations that must be done to determine the correct position of each point. The chaos scientists let the computers draw these graphs and what they got was extraordinary.
They typically observed curves completely different from the “earthquake graph”. Sometimes these curves presented in phase space looked much more as the orbit of a planet around its star. It was as if at a certain point in the phase space there was an invisible axis around which the system moves. Scientists called this invisible focus a “strange attractor”.
This discovery was very important because it allowed us to demonstrate that there is an underlying order in chaos. Yes, the ancient Greek myth was right: order arises from chaos. The conclusion scientists came to is that non-linear systems are not so “chaotic” after all. It all depends on how we look at them: if we look at them from “the front” (earthquake graph) we clearly see their chaotic nature, but if we look at them “in profile” (phase space), like an ugly duckling, their orderly appearance comes to the fore.
In practice this means that, although it is not possible to anticipate the behaviour of a chaotic system, given its strong instability, what can be done is to predict what the system cannot do. When there is a strange attractor, the system has to evolve around it. There is no chance for the system to reach a point outside its path. This is known in chaos theory with the name of asymptotic predictability and it means that the laws of chaos, unlike what happened with deterministic mechanicism, do not force the system to a certain behavior. On the contrary, only pose coarse restrictions in relation to what the system cannot do.
The same happens with living beings and evolution; the environment does not impose on creatures to evolve in any given direction, it only impedes certain conditions. It does not set goals but imposes restrictions on us. The adaptation of species to the environment is very similar to the way in which an individual adapts to his circumstance. Circumstance can never force us to act in one way. There will only be things that we will not be able to do. To survive in our current environment it is very useful to know the laws of chaos. Thanks to them we can cultivate the acceptance of chaos as something natural and stop perceiving it as a threat. After all, it is there, in surprise, in healthy risk, where the true taste of life lies.
