Later that evening I tucked myself under a thick duvet, after having had a hot bath. The guest house was the only one on the island but was of a good standard. The old lady, running it, was shocked to see the state of her guest but readily undertook the tending and care that seemed natural to her. I had a bowl of broth and then retired exhausted.
Under the duvet my body regained its equilibrium and I relaxed. I slept for several hours and when I awoke it was near midnight. I was calm and felt comforted that the incipient headache from my forehead wound had been averted.
I pulled my rucksack over and found my notebook. It was luckily dry, even though the sack’s exterior was still saturated. In the dim light of the bare bulb overhead, I began to write.
Is there reason to chaos? Does it have a teleological end or an ontological beginning? What is chaos? Where there is a lack of order, there is chaos. Nature is full of complex systems. The rocks that form the planet have no order despite their seeming stratification and falling into broad strands of classification. But even this spectacular streaming of beds of limestone or shale across the landscape has all the signs of chaos. There is no predictability arising from their presence. No one can say what the precise future of our landscape will be. This existence of an uncertain future is what makes chaos. There can be an infinity of futures. At most the laws of science can provide models that determine probable futures but for each scenario there is just a single number assigned - the simple probability. Whether the forecast is correct or not remains forever uncertain.
Chaos, being concerned with states in the future, is very much caught up with time. Einstein would probably place it firmly in space-time. But surely the classical laws of Isaac Newton that so elegantly describe the motion of the planets in the solar system deny the prevalence of chaos everywhere? These laws have allowed man to travel to the moon and send spacecraft to Mars and beyond to the outer reaches of the solar system. The very precision of these projects cannot be based on a chaotic environment. The classical laws tame the chaos monster and force it into friendly repetitive behavior. So it appears.
Yet it depends on how a system is viewed. The oceans from space appear a deep calm blue belying the turbulence and chaos of the real seas. Chaos is in the detail: the closer the observation, the more chaotic the dynamics. A feature of chaos is change and therefore it is at the level of the dynamics of the system that one must look for it. For the seas, the scale of dynamics can be that of waves or of currents. In both scales, chaos rules supreme. For geology the dynamics are plate tectonics, rock formation through deposition and volcanic activity - all of which take place on very long timescales and it on these non-familiar timescales that the chaos of the earth’s crust manifests itself.
The weather has always been viewed by humanity as being something that shows no signs of control or firm predictability. At the level of the individual, the timescale of its changes is set at the level of hours or days. Even at these short intervals there is little certitude of the future. What floats across the sky is a small screen of the huge chaotic system that is our atmosphere. The importance of weather to the human psyche has meant that its arbitrary changes have been ascribed to the willful acts of gods denying the underlying chaotic nature. Man was frightened by chaos. It threatened the perceived nature of things - of the link between cause and effect. The evolution of homo sapiens was the birth of the concept of free will. Up to this all living creatures reacted passively to their environment coping and surviving on a fittest basis. Because they had not cognitive skills they could not stand back from the environment and see themselves situated within it. It was the evolution of the ability to see themselves as individuals - to know that they existed - that allowed mankind to start to react in an active manner to the environment. The shroud of animalistic blindness was removed and the brilliant wild beauty of the world was revealed. This early revelation was of a chaotic beauty. There were no reasons for events. Lightening spears across the sky were portents of the unknown. In this sea of uncertainty man started to make small progress at shaping or controlling his world. He shaped stones into sharp weapons that could be used in hunting. He learnt that by using lessons from the past that he could better control the future. The weapon making skills were honed. In all of this the laws of a cause leading to an effect were becoming ingrained.
It is natural that we prefer to live in a sure world where we can predict the future. Long eons of human evolution have imprinted it into our genetic make up. We are programmed to look for order. We seek out symmetries, orderliness, repetition, synchronism and longevity. It seems that we view the world with special glasses that filter out the chaotic and give a Polaroid view of a world full of predictable laws. This had its peak in the post Newtonian era when it was felt that the whole universe was determinate. If one could fix the location and motion of every particle in the universe at a particular time then it would be possible to specify the entire universe not just in the past but also into the future. The past held the data to divine laws that fully determined the future.
The way we view the world has huge impact on our philosophy of life. If we believe in the concept of free will, our philosophy will be full of ethics defining our correct behaviors, given this sublime freedom. The medieval world was dominated by religious beliefs that espoused the fires of hell as awaiting those who transgressed the revealed laws of Christianity. The horror of eternity in hell was no longer a plausible scenario if there was no free will. The deterministic reality underlying Newton’s physical model released humanity from the hellfire but placed him in a straitjacket of strict passivity. As a free agent he was able to carve out an individual path for himself but under Newton that path was already decided and set in stone. There was not much point in thinking too much about how he behaved as it was already determined for him.
It was really the advent of the first ideas of quantum mechanics in the early twentieth century that broke the linkage with the Newtonian paradigm of strict determinism. Just as when you look at the oceans from space the chaos of the surface is not revealed, so looking at the planetary motions with Newtonian eyes hides the underlying space-time. Newton saw the planets moving in a Euclidean space of three dimensions and their motions measured using an absolute time that is the same throughout the universe. Einstein saw the planets moving in space-time where both time and space is relative to the speed of the observer. Newton’s vantage point was fixed firmly on Earth and instantaneous; Einstein’s was located at the outer reaches of the universe and spanned the scale of time. From his strange vantage point Einstein was able to see the topology of space-time. He was able to see that space-time was curved up into strange shapes that morphed into each other. He gave humanity the eyes to see the shapes of chaos yet his laws were still deterministic and at the level of human reality were just those same laws as discovered by Newton.
The eyes of the quantum world were at inverse scales to those of Einstein. They looked at the world at Planck distances of very much less than the size of an atom and at incredibly small Planck times. Here the world was lumpy and wavy at the same time, introducing uncertainty. In fact Heisenberg’s Uncertainty Principle - that you could not co-measure location and motion to beyond a certain precision at the Planck scale - meant that reality of the present became uncertain. Determinism was now under challenge. If you cannot define the precise present, no matter what laws you use, the future will be uncertain. Uncertainty in , uncertainty out. Chaos had been restored to the world but only at this microscopic level. Once you accepted this uncertainty of initial conditions then the laws - in this case the Schrodinger law of evolution - would give deterministic behavior at the classical level. The laws of quantum theory had to reveal the classical laws at the macro level.
But modern studies of chaos have shown that the response of some systems to small imprecision in the initial conditions can lead to complex, unpredictable behavior. The flapping of a butterfly’s wings in China can lead to hurricanes in Florida. Even very s
imple systems can become unpredictable if there are small changes in the initial conditions. Chaos is everywhere because of our inability to measure reality precisely. If we cannot know the present, how can we tell the future?
Chaos has restored freewill. The outcome of our actions is uncertain. How we act has consequences most of which we will never know and most of which we can never possibly know. Yet the laws of science do tell us that certain consequences are at least probable and in many cases almost certain. The coin let fall from our hand goes down, not up. This is true in most of our realities. Yet some modern realities have shown that there are cases where the coin floats. For this to happen you have to have the highly improbable circumstance that you find yourself in a spaceship orbiting the earth. Yet you have the free will to make that reality happen. You make yourself fit, educate yourself and maybe adopt American or Russian citizenship. The chance reading of a science fiction book as a kid may be the small flap of a butterfly’s wing that propels you into space and a world where coins float.
Who knows maybe you are already in a world where coins float. The weird world of quantum theory has concocted such scenarios. Because of the Uncertainty Principle we can only describe the world in probabilistic terms. This leads to a spectrum of possibilities each with its own likelihood or amplitude. This generates a wave model of multiple realities each with a probability. When we make an observation only one reality emerges. Yet some theorists propose that all the others co-exist but are not accessible to us. This can be extrapolated to the concept of multiple universes each with their own Big Bang, each emerging from a froth on the ocean of greater reality. This froth is the ultimate chaos.
The philosophy that emerges from all this science and, in the case of multiverses - speculation, is still in formation. Whatever emerges will most likely be a philosophy of action. The realization that all our actions can have big consequences should make us more circumspect when we decide to try something new. Our past actions have been tried and tested. Sometimes the response indicators are very lagging. The effect on the environment of the huge rush to burn fossil fuels in the twentieth century may be chaotic. One of the features of chaotic systems is that the chaos can be hidden for long periods and then the system can suddenly flip to a new condition without any warning. Scientists have been debating for decades on the global threat of greenhouse gases and have not found definitive proof of the environment changing other than it might have done as part of its natural cycling. Yet the change may be waiting to flip. Can our actions prevent it? The butterfly has already flapped his wings. Our philosophy of action says we must try. We can influence our future by our present actions. It is only the determinists who would recommend inaction.
More than action is required of a philosophy. It needs to address the existential loneliness of the human spirit. How can knowledge of the serendipity of the future be a solace or support to the spirit? We are here by chance and where we end up is all chance, albeit while here on earth we can force the issue a bit and become the prescribed astronaut or doctor or whatever. The human spirit seeks direction in terms of a future. Purpose and future are intertwined. A purpose without future is a contradiction. How does a chaotic future affect our sense of purpose? We look into the future and discern the parts that appeal to us. If we are young we see getting our first job or getting married or starting a family. In middle life we see promotion, eventual retirement or perhaps grandchildren. In old age we tend not to see the future. We see a shortening remnant of a life. The unpredictable end is nearing. Death is becoming more probable. We start to question beyond death. The religious among us simply accept the paradigm of the joining up with God or Heaven, yet the specifics of this are never teased out. The atheist sees a simple end to a life.
Chaos is continuous unpredictable change and underpins all reality. The human existence is an immeasurably small part of this reality. Being so small does not necessarily mean that the individual person cannot flap his wings. Each human existence does impact on the cosmos. What separates the human existence from other non-thinking events is the fact that humans have free will. They can place themselves in their environment and act independently - as if outside the normal laws of science. They become the special observers in the quantum world whose intervention causes the wave of possibilities of reality to collapse into their own almost solipsistic universe. It is solipsistic, as the individual is the only one who can experience it. Awareness of the universe places humanity in a very privileged place in the space-time of our cosmos. The earth has no special position in space but has a very special position in space-time - a vantage point that reveals billions of universes, one for each person born since the dawn of evolution. These universes are born and die with the body. They are not totally independent but overlap and tangle chaotically. Each can leave its mark on the greater universe or cosmos that evolves on a much vaster scale.
If we take it that we live in this island of billions of micro-universes in the vast ocean of the greater universe, it follows that the greater universe is a solipsistic universe of a single being. But this reasoning is endless, as that greater being may also live on an island of billions of beings in a far greater universe. The world picture has become overcomplicated. There is no end point to the speculation. Rationality has been lost. Yet the flap of a butterfly’s wing is immensely remote from storms over Florida.
The only very recent focus of the scientific community on chaos is evidence of how myopic culture can sometimes become. Science has set its stall in searching for simple laws that short circuit complex behavior to give predicted results. The problem for the world of knowledge is that such efforts constrain activity to very simple systems that display minimal complexity. The cold realization is that most of the systems in nature are utterly irreducible in terms of their computational complexity. This means that, say, the evolutionary history of the bumble bee cannot be summarized into a short program so that after a set number of computations out pops the completed insect. The hard reality is that the bee is the result of trillions of computations over trillions of generations. Each generation applies some as yet unknown basic ‘bee’ rules to the constraints imposed by the environment at that time. The aim is still survival against the background of the environment. The bumble bee as we now see him is a work in progress. The idea that an optimum ‘bee’ has been attained, despite the obvious beauty of the insect, is far from being achieved and indeed can never be achieved. To meet the requirements of optimum survival form the bee would need more computational runs or generations of lineage than there are particles in the entire known universe!
The bee is certainly a very complex organism and we have to concede that we can never recreate its beauty computationally. That does not mean that we should not strive to understand and divine the underlying rules or laws of ‘bee-ness’ or any other system. The fact that many simple systems generate chaos or complex unpredictable behavior gives a hint that the underlying rules for bees may be quite simple. For example the color texture of the bee can be simply modeled computationally from a few basic rules. The paradox of the ‘bee’ example is that to us the bee does not appear disordered or especially complex. In fact it is the external environment that has forged the bee that is chaotic and random. The bee evolves as an ordered state in a chaotic world but it is as attached to the world as a baby is connected to its mother’s body by its umbilical chord. Without the external environment there would be no ‘bee’.
The same line of thinking can be applied to all living things, even to homo sapiens. The major difference with man is that through his self awareness he can react actively to his environment and this in turn adds an infinitude of further complexity. Men and women are indeed very complex animals! They have to be viewed not by invoking simple rules for behavior but from the perspective of the billions of years of evolutionary history where each generation of ancestors struggled with the external environment. The digits of my hands are linked in a causal chain all the way back to the primi
tive fish that first migrated from sea to land. Each of the billions of steps has to be taken to arrive at the dexterity of these typing fingers. There is no short cut or rule of thumb to cut out the slog of reality. Science will never develop a ‘finger’ law complete with exponentials, complex numbers and high order partial differential equations. Such a law can only describe simple systems.
If science is toothless in describing the real world of complex systems why bother at all? It is not as hopeless as it sounds. All knowledge is based on perception and analysis, in the fervent hope of reordering the data into bite size understandable chunks. The human brain, magnificent though it is, has not the capacity to store all its inputs. It must choose and link data and then store the key links. In doing this it filters all but a tiny percentage of all incoming perception. It then tries to categorize the information in terms of language. The concept of ‘bird’ retains its general features of ‘beakiness’ or ‘featheriness’ or whatever. It then tries to link the stored data and form of language emerges in terms of subject and object. The dynamics of the external environment then lead to the development of language in terms of action verbs. These are primitive statements of law that describe the real world.
But these words and verbs have their realization in the external environment. The developing brain now tries to fix the words in space and the rules of geometry emerge. The movement of words in space lead to the development of dynamic laws. Science can thus be seen as a natural evolution of language. Like language it tries to filter and simplify. Most sciences do this quite unashamedly. For instance the science of fluid dynamics spends a lot of time studying laminar flow where the fluid flows in perfect parallel layers. This does not occur very often in reality but is simple and easy to study. Real life flow is turbulent, it flows in wild unpredictable eddies and is not susceptible to simple analysis. One can see similar patterns in thermodynamics where the famous second law contends that entropy, a measure of disorder in a system, always increases with evolving time. This science emerged from the study of gases but only by disconnecting from the external environment. The closed systems of thermodynamics are far removed from the complexity of real life. In fact biology shows striking contrary behavior in developing order out of disorder. No one has yet explained why order should emerge from disorder. Incredibly our world is full of islands of order in an otherwise disordered universe.
Science, in trying to apply simple rules to lend predictability to small parts of our world, is at the first step of a long journey of discovery. This was a totally necessary step and will always yield good results in terms of technology advance. Conventional science in that sense will always predominate and be of great value to humanity.
Yet, even now, a new quiet revolution is taking place. The continuing advance of computer power has changed the paradigm. The huge computing capability of the internet allows analysis of complex systems for the first time. There is still the same restraint that a complex system is irreducible into smaller computational steps but the increasing computational world resource available in all the linked computers, allows scientists to run portions of evolution of systems under study. It will be like unlocking a secret corner of chaos. It will represent a paradigm shift in science for the first time, away from the business of simplifying but now focusing on the chaotic environment in which the islands of simple order float.
The paradigm shift is one of holism. To study chaotic systems you have to encompass the entire evolution of the system and that ultimately leads to studying the entire evolution of the cosmos. The thinking becomes one of linkage rather than one of isolation. Reductionism, which for so long was a very productive paradigm, may have had its day.
Five
Morbid Space